This document discusses strategies for maximizing fracture toughness through microstructure design. It explains that toughness can be increased by minimizing defects like cracks, and by designing microstructures that require additional energy to propagate cracks. Specific strategies discussed include laminating materials to deflect cracks, adding stiff fibers for crack bridging, including particles that transform under stress or microcrack to absorb energy, and minimizing grain size to reduce maximum crack size. The document also notes that optimization of toughness often requires balancing strength, and discusses approaches for characterizing crack size distributions.
Strengthening mechanisms in metals include work hardening, solid solution strengthening, and precipitation hardening. Work hardening increases yield strength by introducing dislocations through plastic deformation, which impede further dislocation movement. Solid solution strengthening adds solute atoms that distort the crystal lattice and interfere with dislocations. Precipitation hardening involves heat treating alloys to form precipitates that impede dislocations. These mechanisms strengthen metals by making dislocation motion and propagation more difficult.
Introduction to Mechanical Metallurgy (Our course project)Rishabh Gupta
The document summarizes key concepts in materials science and engineering. It discusses:
1. The importance of selecting high quality materials for better product design and performance.
2. The four main components in materials science - processing, structure, properties, and performance - and how they interrelate.
3. The main classes of materials - metals, ceramics, polymers, composites, semiconductors, and elastomers - and some of their key characteristics.
4. Crystal structures of metals and how they are classified based on atomic packing efficiency. Factors that determine a material's density are also covered.
This document summarizes key concepts about mechanical failure from chapter 8, including:
1. It discusses different failure mechanisms like fracture, fatigue, creep, corrosion, and others. It also defines ductile and brittle fracture.
2. Fatigue failure is described as occurring in three stages - crack initiation, propagation, and final failure. It is influenced by factors like stress range and mean stress.
3. Fracture toughness is introduced as a material's resistance to brittle fracture when a crack is present. The influence of loading rate, temperature, and microstructure on failure stress is also covered.
DJJ3213 MATERIAL SCIENCE CHAPTER 3 NOTE.pptfieyzaadn
This document summarizes various mechanical properties and failure modes of materials. It defines physical, thermal, and mechanical properties. Thermal properties describe a material's response to heat, such as heat capacity and thermal expansion. Mechanical properties describe how a material reacts to forces and include properties like toughness, hardness, and elasticity. Failure modes like fracture, fatigue, and creep are also discussed. The document contrasts ductile and brittle failure, and describes how properties vary with temperature for different materials. It provides examples of different fracture surfaces and discusses fracture mechanics concepts.
FRACTURE BEHAVIOUR OF NANOCOMPOSITES -FATIGUEArjun K Gopi
This document discusses the fracture and fatigue behavior of polymer nanocomposites. It notes that nanoparticles have higher specific surface areas than microparticles, which can improve stress transfer and that nanoparticles can be added at lower loadings while retaining properties of the neat polymer matrix. The document covers different types of fractures like brittle and ductile, and describes how the addition of nanoparticles up to 5 wt% can improve the fatigue resistance of polyamide nanocomposites by inhibiting crack propagation, but higher loadings may embrittle the material. TEM images show the differences in clay dispersion with varying nanoparticle content.
The document summarizes key concepts related to failure of materials including the three main failure modes: fracture, fatigue, and creep. It defines fracture as failure due to crack propagation, fatigue as failure under cyclic loading even when maximum stresses are below the material's strength, and creep as progressive deformation under constant stress at elevated temperatures. The summary provides examples of each failure mode and discusses testing techniques like impact, fatigue, and creep tests used to characterize failure behavior. Fracture mechanics concepts like stress concentration and fracture toughness are also introduced for understanding crack propagation and designing against failure.
The document discusses various structural design principles and concepts including:
- Robustness, strength, serviceability, and stability as key structural principles.
- Defining ultimate stress and hardness as material properties.
- How materials behave after exceeding their yield strength on a stress-strain curve.
- Critical considerations for material selection like mechanical properties, wear resistance, and cost.
- Calculating axial tensile stress on a steel column given its dimensions and applied load.
- Engineer must consider member weights and load variations when determining dead and live loads.
- Limit state design uses a two-layered safety approach to determine load capacities.
Due to dislocations, it is no longer necessary to break all bonds between two atomic planes at once in order to shear off a lattice planes.
Rather, it is enough to overcome only one binding series at a time.
The dislocation line jumps step-by-step from atomic row to atomic row with little effort and finally emerges as a slip step on the surface of the material.
Strengthening mechanisms in metals include work hardening, solid solution strengthening, and precipitation hardening. Work hardening increases yield strength by introducing dislocations through plastic deformation, which impede further dislocation movement. Solid solution strengthening adds solute atoms that distort the crystal lattice and interfere with dislocations. Precipitation hardening involves heat treating alloys to form precipitates that impede dislocations. These mechanisms strengthen metals by making dislocation motion and propagation more difficult.
Introduction to Mechanical Metallurgy (Our course project)Rishabh Gupta
The document summarizes key concepts in materials science and engineering. It discusses:
1. The importance of selecting high quality materials for better product design and performance.
2. The four main components in materials science - processing, structure, properties, and performance - and how they interrelate.
3. The main classes of materials - metals, ceramics, polymers, composites, semiconductors, and elastomers - and some of their key characteristics.
4. Crystal structures of metals and how they are classified based on atomic packing efficiency. Factors that determine a material's density are also covered.
This document summarizes key concepts about mechanical failure from chapter 8, including:
1. It discusses different failure mechanisms like fracture, fatigue, creep, corrosion, and others. It also defines ductile and brittle fracture.
2. Fatigue failure is described as occurring in three stages - crack initiation, propagation, and final failure. It is influenced by factors like stress range and mean stress.
3. Fracture toughness is introduced as a material's resistance to brittle fracture when a crack is present. The influence of loading rate, temperature, and microstructure on failure stress is also covered.
DJJ3213 MATERIAL SCIENCE CHAPTER 3 NOTE.pptfieyzaadn
This document summarizes various mechanical properties and failure modes of materials. It defines physical, thermal, and mechanical properties. Thermal properties describe a material's response to heat, such as heat capacity and thermal expansion. Mechanical properties describe how a material reacts to forces and include properties like toughness, hardness, and elasticity. Failure modes like fracture, fatigue, and creep are also discussed. The document contrasts ductile and brittle failure, and describes how properties vary with temperature for different materials. It provides examples of different fracture surfaces and discusses fracture mechanics concepts.
FRACTURE BEHAVIOUR OF NANOCOMPOSITES -FATIGUEArjun K Gopi
This document discusses the fracture and fatigue behavior of polymer nanocomposites. It notes that nanoparticles have higher specific surface areas than microparticles, which can improve stress transfer and that nanoparticles can be added at lower loadings while retaining properties of the neat polymer matrix. The document covers different types of fractures like brittle and ductile, and describes how the addition of nanoparticles up to 5 wt% can improve the fatigue resistance of polyamide nanocomposites by inhibiting crack propagation, but higher loadings may embrittle the material. TEM images show the differences in clay dispersion with varying nanoparticle content.
The document summarizes key concepts related to failure of materials including the three main failure modes: fracture, fatigue, and creep. It defines fracture as failure due to crack propagation, fatigue as failure under cyclic loading even when maximum stresses are below the material's strength, and creep as progressive deformation under constant stress at elevated temperatures. The summary provides examples of each failure mode and discusses testing techniques like impact, fatigue, and creep tests used to characterize failure behavior. Fracture mechanics concepts like stress concentration and fracture toughness are also introduced for understanding crack propagation and designing against failure.
The document discusses various structural design principles and concepts including:
- Robustness, strength, serviceability, and stability as key structural principles.
- Defining ultimate stress and hardness as material properties.
- How materials behave after exceeding their yield strength on a stress-strain curve.
- Critical considerations for material selection like mechanical properties, wear resistance, and cost.
- Calculating axial tensile stress on a steel column given its dimensions and applied load.
- Engineer must consider member weights and load variations when determining dead and live loads.
- Limit state design uses a two-layered safety approach to determine load capacities.
Due to dislocations, it is no longer necessary to break all bonds between two atomic planes at once in order to shear off a lattice planes.
Rather, it is enough to overcome only one binding series at a time.
The dislocation line jumps step-by-step from atomic row to atomic row with little effort and finally emerges as a slip step on the surface of the material.
Mechanical properties of ceramics are determined using bending tests rather than tensile tests due to their brittle nature. Ceramics experience negligible plastic deformation and fracture at low strains. Their strength is significantly impacted by flaws which act as stress concentrators. Fracture toughness characterizes a ceramic's resistance to crack propagation and is used to determine the maximum stress before failure for a given flaw size. The stochastic nature of flaws leads to significant variation in measured fracture strengths between specimens of the same material.
This chapter introduces fundamental concepts in materials science and engineering. It discusses how material structure dictates properties and how processing can change structure. The goals of the course are to help students use materials properly, understand the relationship between properties, structure and processing, and recognize new design opportunities using materials selection. Key concepts covered include material structure, properties, and processing and how they influence one another.
Stress-Strain Curves for Metals, Ceramics and PolymersLuís Rita
Homework II - Biomaterials Science
We are interested about studying and comparing stress-strain curves of metals, ceramics and polymers. Primarily, differences are due to their different chemical bonding properties.
IST - 4th Year - 2nd Semester - Biomedical Engineering.
This document contains questions and answers related to structural design principles. It discusses key concepts like robustness, strength, serviceability, stability, material properties, structural analysis, different load types, limit state design, and structural systems. Questions cover topics such as structural principles, material properties, stress-strain behavior, load considerations, deflection calculations, tributary areas, concrete beam design, reinforced and prestressed concrete, vibration causes and solutions, soil properties, retaining walls, ground improvement techniques, and foundation systems.
This summary provides an overview of the key structural concepts covered in the document:
1. The document discusses various structural principles including robustness, strength, serviceability, and stability and provides examples for each. It also defines material properties like ultimate stress and hardness.
2. Load types such as permanent loads, live loads, and wind loads are described along with considerations for determining their magnitude.
3. Limit state design and the two-layered factor of safety approach are explained. Limit state design uses modern methods to determine structural capacity and loading.
4. Stability systems like braced frames are discussed as ways to provide stability to structures subjected to lateral loads. The GLAD workflow for structural design is
Metallic materials can undergo elastic or plastic deformation when stressed. Plastic deformation is permanent and corresponds to the movement of dislocations on an atomic scale. Several mechanisms can strengthen materials by impeding dislocation movement, such as grain refinement, solid solution strengthening, and strain hardening. Grain refinement strengthens materials by introducing more grain boundaries that act as barriers to dislocation motion. Solid solution strengthening occurs when alloying elements are added, which impose lattice strains and interact with dislocations. Strain hardening makes metals stronger through plastic deformation, which increases dislocation density and hinders their movement.
Composites are materials made from two or more constituent materials with different physical or chemical properties. The materials remain separate within the finished structure to produce properties that are superior to those of the individual components. Composites consist of a reinforcement material, such as fibers, sheets or particles, embedded within a matrix material that maintains the relative positions of the reinforcements and allows for load transfer from the matrix to the reinforcement. Common reinforcement materials include glass, carbon and organic fibers while matrix materials include polymers, metals and ceramics. Composites offer advantages over traditional materials like high strength, light weight, design flexibility and resistance to corrosion.
The document discusses the impact performance of plastics. It begins by defining impact strength as a plastic's ability to withstand a rapidly applied load. It then describes how impact performance depends on temperature and loading rate, with most plastics behaving brittle at low temperatures and high loading rates, and ductile at high temperatures and low loading rates. This transition from ductile to brittle failure with changing conditions is known as the ductile-brittle transition. The document outlines common impact testing methods and explains how the test results do not always directly translate to predicting a material's impact performance in a final product.
There are several mechanisms that can strengthen materials by hindering the movement of dislocations:
1) Grain size reduction - Smaller grain sizes provide more barriers to dislocation movement at grain boundaries. According to the Hall-Petch relationship, smaller grain diameters yield higher yield strengths.
2) Solid solution strengthening - Impurity atoms distort the crystal lattice and generate stress fields that impede dislocation motion. The effectiveness depends on size difference and concentration of solute atoms.
3) Strain hardening - Plastic deformation increases dislocation density within a material, making further dislocation movement more difficult through interactions between dislocations. This causes strain hardened metals to strengthen with increasing plastic deformation.
This document contains a lesson plan and materials for an engineering materials course. The lesson plan outlines 12 topics to be covered across 12 weeks, including introduction to materials and atomic bonding, mechanical properties testing, tribology, fatigue analysis, corrosion, metals and alloys, polymers and ceramics, materials selection, and revision. Key concepts and learning objectives are defined for each topic. The document also provides examples and explanations to supplement the lesson content, such as definitions of toughness, descriptions of impact testing methods, diagrams of stress-strain curves for ceramics, and examples of calculating flexural strength and modulus from three-point bending tests. References for the course materials are also listed.
Tribological study of Ceramic Matrix Composite(CMCs).pptxShibaSankarDash
Ceramic matrix composites (CMCs) have improved fracture toughness over conventional structural ceramics through the addition of fibers that increase crack resistance. This document discusses the tribological properties and wear mechanisms of various CMCs, including those reinforced with silicon carbide (SiC) fibers in a silicon nitride (Si3N4) matrix or carbon fibers in a silicon carbide (SiC) matrix. The lowest wear rates were found for zirconium diboride (ZrB2) composites containing 8-32% aluminum oxide (Al2O3). Proper material selection and microstructure optimization can improve CMC reliability and performance in tribological applications.
This document discusses material selection and properties in three chapters. Chapter 3 introduces material classes, defining properties important for mechanical design like modulus, strength, damping capacity, and thermal conductivity. The main material classes are metals, polymers, ceramics, glasses, and composites. Metals have high modulus but can fatigue. Ceramics and glasses are also stiff but brittle. Polymers have low modulus but are strong and easy to shape. Composites combine advantages but have limitations. Definitions of properties like density, modulus, strength, and toughness are also provided.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Experimental Study of the Fatigue Strength of Glass fiber epoxy and Chapstan ...IJMER
1) The document describes an experimental study of the fatigue strength of two types of fiber-reinforced epoxy composite laminates: glass fiber epoxy and E-glass epoxy.
2) The study developed a fatigue testing rig to apply cyclic bending loads to composite beam specimens and measure the resulting stiffness degradation over cycles until failure.
3) The testing rig incorporated a load cell, data acquisition system, and software to automatically record measurements over millions of load cycles and analyze the failure behavior and fatigue life of the composite laminates.
Experimental evaluations and performance of the aluminum silicon carbide par...IAEME Publication
This document summarizes an experimental study on aluminum-silicon carbide particle metal matrix composites. Ring-shaped composites were fabricated using solid-state processing with varying sintering temperatures and times. The composites were subjected to thermal shock at +800C and -800C, and their radial crushing strength was tested. Micrographs of the fractured surfaces were analyzed. Thermal shock from sub-ambient temperatures was found to be more damaging than from elevated temperatures. Failure from elevated temperatures was dominated by cavity formation at interfaces, while sub-ambient temperatures caused more interfacial and matrix damage. The study evaluated the effect of reinforcement particles on the mechanical properties of the composites.
Experimental evaluations and performance of the aluminum silicon carbide par...IAEME Publication
Stresses induced due to thermal mismatch between the metal matrix and the ceramic reinforcement in metal matrix composite may impart plastic deformation to the matrix there by
resulting in a reduction of the residual stresses. Thermal mismatch strains also may quite often crack
the matrix resulting in a relaxation of the residual stresses. The interface in MMCs is a porous, noncrystalline portion in comparison with the matrix or the reinforcement (metal matrix and ceramic reinforcement in this case).
Strain hardening occurs when dislocations in a deformed metal interact, increasing the material's strength. Deforming a metal increases the number of dislocations, further strengthening the material. Strain hardening is measured by properties like yield strength and tensile strength increasing while ductility decreases. The material becomes harder but more brittle. Annealing can be used to "undo" strain hardening by allowing dislocations to rearrange or new grains to form, restoring ductility at the cost of strength. The annealing process involves recovery, recrystallization and sometimes grain growth, and depends on temperature and time.
Under repeated impact composite domes subjected 6 J energy, changes locally with
increasing drop height. The action of the dynamic load generates reactions at the
support and bending moments at points on the surface of the composite. The peak loads
were noted to increase and stabilise about some mean value; and the 150mm diameter
shell was more damage tolerant compared to the 200 mm diameter one.
Experimental composite dome under low velocity impact loadalilimam2
The document summarizes a study that characterized the impact response of glass fiber reinforced composite dome structures with diameters of 150mm and 200mm under repeated low-energy impacts. Key findings include:
1) Peak impact loads initially increased and stabilized with repeated impacts, and the 150mm diameter dome showed higher peak loads and was more damage tolerant.
2) Damage mechanisms included matrix cracking, delamination, and fiber pull-out. Delamination absorbed a large percentage of the impact energy.
3) Both dome configurations exhibited non-linear impact behavior, with stiffness reducing and energy dissipation decreasing with accumulated damage from repeated impacts.
Este documento describe los procesos de solidificación que ocurren en las piezas fundidas. Explica que durante la solidificación hay cambios volumétricos, segregaciones y la formación de macro y microestructuras. También describe cómo la estructura de granos depende del sistema de aleación, composición, temperatura de colada y tipo de molde. Finalmente, introduce conceptos como el módulo de enfriamiento y cómo este afecta el orden y velocidad de solidificación.
El documento describe el Análisis del Modo de Falla y sus Efectos (AMFE), una herramienta para identificar y prevenir fallas potenciales. Se desarrolló originalmente para la industria aeroespacial en los años 1970 y desde entonces se ha aplicado a una variedad de industrias. El AMFE involucra un análisis sistemático de un grupo multidisciplinario para detectar fallas potenciales, evaluar sus efectos, y determinar acciones para eliminar o reducir las probabilidades de falla.
Mechanical properties of ceramics are determined using bending tests rather than tensile tests due to their brittle nature. Ceramics experience negligible plastic deformation and fracture at low strains. Their strength is significantly impacted by flaws which act as stress concentrators. Fracture toughness characterizes a ceramic's resistance to crack propagation and is used to determine the maximum stress before failure for a given flaw size. The stochastic nature of flaws leads to significant variation in measured fracture strengths between specimens of the same material.
This chapter introduces fundamental concepts in materials science and engineering. It discusses how material structure dictates properties and how processing can change structure. The goals of the course are to help students use materials properly, understand the relationship between properties, structure and processing, and recognize new design opportunities using materials selection. Key concepts covered include material structure, properties, and processing and how they influence one another.
Stress-Strain Curves for Metals, Ceramics and PolymersLuís Rita
Homework II - Biomaterials Science
We are interested about studying and comparing stress-strain curves of metals, ceramics and polymers. Primarily, differences are due to their different chemical bonding properties.
IST - 4th Year - 2nd Semester - Biomedical Engineering.
This document contains questions and answers related to structural design principles. It discusses key concepts like robustness, strength, serviceability, stability, material properties, structural analysis, different load types, limit state design, and structural systems. Questions cover topics such as structural principles, material properties, stress-strain behavior, load considerations, deflection calculations, tributary areas, concrete beam design, reinforced and prestressed concrete, vibration causes and solutions, soil properties, retaining walls, ground improvement techniques, and foundation systems.
This summary provides an overview of the key structural concepts covered in the document:
1. The document discusses various structural principles including robustness, strength, serviceability, and stability and provides examples for each. It also defines material properties like ultimate stress and hardness.
2. Load types such as permanent loads, live loads, and wind loads are described along with considerations for determining their magnitude.
3. Limit state design and the two-layered factor of safety approach are explained. Limit state design uses modern methods to determine structural capacity and loading.
4. Stability systems like braced frames are discussed as ways to provide stability to structures subjected to lateral loads. The GLAD workflow for structural design is
Metallic materials can undergo elastic or plastic deformation when stressed. Plastic deformation is permanent and corresponds to the movement of dislocations on an atomic scale. Several mechanisms can strengthen materials by impeding dislocation movement, such as grain refinement, solid solution strengthening, and strain hardening. Grain refinement strengthens materials by introducing more grain boundaries that act as barriers to dislocation motion. Solid solution strengthening occurs when alloying elements are added, which impose lattice strains and interact with dislocations. Strain hardening makes metals stronger through plastic deformation, which increases dislocation density and hinders their movement.
Composites are materials made from two or more constituent materials with different physical or chemical properties. The materials remain separate within the finished structure to produce properties that are superior to those of the individual components. Composites consist of a reinforcement material, such as fibers, sheets or particles, embedded within a matrix material that maintains the relative positions of the reinforcements and allows for load transfer from the matrix to the reinforcement. Common reinforcement materials include glass, carbon and organic fibers while matrix materials include polymers, metals and ceramics. Composites offer advantages over traditional materials like high strength, light weight, design flexibility and resistance to corrosion.
The document discusses the impact performance of plastics. It begins by defining impact strength as a plastic's ability to withstand a rapidly applied load. It then describes how impact performance depends on temperature and loading rate, with most plastics behaving brittle at low temperatures and high loading rates, and ductile at high temperatures and low loading rates. This transition from ductile to brittle failure with changing conditions is known as the ductile-brittle transition. The document outlines common impact testing methods and explains how the test results do not always directly translate to predicting a material's impact performance in a final product.
There are several mechanisms that can strengthen materials by hindering the movement of dislocations:
1) Grain size reduction - Smaller grain sizes provide more barriers to dislocation movement at grain boundaries. According to the Hall-Petch relationship, smaller grain diameters yield higher yield strengths.
2) Solid solution strengthening - Impurity atoms distort the crystal lattice and generate stress fields that impede dislocation motion. The effectiveness depends on size difference and concentration of solute atoms.
3) Strain hardening - Plastic deformation increases dislocation density within a material, making further dislocation movement more difficult through interactions between dislocations. This causes strain hardened metals to strengthen with increasing plastic deformation.
This document contains a lesson plan and materials for an engineering materials course. The lesson plan outlines 12 topics to be covered across 12 weeks, including introduction to materials and atomic bonding, mechanical properties testing, tribology, fatigue analysis, corrosion, metals and alloys, polymers and ceramics, materials selection, and revision. Key concepts and learning objectives are defined for each topic. The document also provides examples and explanations to supplement the lesson content, such as definitions of toughness, descriptions of impact testing methods, diagrams of stress-strain curves for ceramics, and examples of calculating flexural strength and modulus from three-point bending tests. References for the course materials are also listed.
Tribological study of Ceramic Matrix Composite(CMCs).pptxShibaSankarDash
Ceramic matrix composites (CMCs) have improved fracture toughness over conventional structural ceramics through the addition of fibers that increase crack resistance. This document discusses the tribological properties and wear mechanisms of various CMCs, including those reinforced with silicon carbide (SiC) fibers in a silicon nitride (Si3N4) matrix or carbon fibers in a silicon carbide (SiC) matrix. The lowest wear rates were found for zirconium diboride (ZrB2) composites containing 8-32% aluminum oxide (Al2O3). Proper material selection and microstructure optimization can improve CMC reliability and performance in tribological applications.
This document discusses material selection and properties in three chapters. Chapter 3 introduces material classes, defining properties important for mechanical design like modulus, strength, damping capacity, and thermal conductivity. The main material classes are metals, polymers, ceramics, glasses, and composites. Metals have high modulus but can fatigue. Ceramics and glasses are also stiff but brittle. Polymers have low modulus but are strong and easy to shape. Composites combine advantages but have limitations. Definitions of properties like density, modulus, strength, and toughness are also provided.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Experimental Study of the Fatigue Strength of Glass fiber epoxy and Chapstan ...IJMER
1) The document describes an experimental study of the fatigue strength of two types of fiber-reinforced epoxy composite laminates: glass fiber epoxy and E-glass epoxy.
2) The study developed a fatigue testing rig to apply cyclic bending loads to composite beam specimens and measure the resulting stiffness degradation over cycles until failure.
3) The testing rig incorporated a load cell, data acquisition system, and software to automatically record measurements over millions of load cycles and analyze the failure behavior and fatigue life of the composite laminates.
Experimental evaluations and performance of the aluminum silicon carbide par...IAEME Publication
This document summarizes an experimental study on aluminum-silicon carbide particle metal matrix composites. Ring-shaped composites were fabricated using solid-state processing with varying sintering temperatures and times. The composites were subjected to thermal shock at +800C and -800C, and their radial crushing strength was tested. Micrographs of the fractured surfaces were analyzed. Thermal shock from sub-ambient temperatures was found to be more damaging than from elevated temperatures. Failure from elevated temperatures was dominated by cavity formation at interfaces, while sub-ambient temperatures caused more interfacial and matrix damage. The study evaluated the effect of reinforcement particles on the mechanical properties of the composites.
Experimental evaluations and performance of the aluminum silicon carbide par...IAEME Publication
Stresses induced due to thermal mismatch between the metal matrix and the ceramic reinforcement in metal matrix composite may impart plastic deformation to the matrix there by
resulting in a reduction of the residual stresses. Thermal mismatch strains also may quite often crack
the matrix resulting in a relaxation of the residual stresses. The interface in MMCs is a porous, noncrystalline portion in comparison with the matrix or the reinforcement (metal matrix and ceramic reinforcement in this case).
Strain hardening occurs when dislocations in a deformed metal interact, increasing the material's strength. Deforming a metal increases the number of dislocations, further strengthening the material. Strain hardening is measured by properties like yield strength and tensile strength increasing while ductility decreases. The material becomes harder but more brittle. Annealing can be used to "undo" strain hardening by allowing dislocations to rearrange or new grains to form, restoring ductility at the cost of strength. The annealing process involves recovery, recrystallization and sometimes grain growth, and depends on temperature and time.
Under repeated impact composite domes subjected 6 J energy, changes locally with
increasing drop height. The action of the dynamic load generates reactions at the
support and bending moments at points on the surface of the composite. The peak loads
were noted to increase and stabilise about some mean value; and the 150mm diameter
shell was more damage tolerant compared to the 200 mm diameter one.
Experimental composite dome under low velocity impact loadalilimam2
The document summarizes a study that characterized the impact response of glass fiber reinforced composite dome structures with diameters of 150mm and 200mm under repeated low-energy impacts. Key findings include:
1) Peak impact loads initially increased and stabilized with repeated impacts, and the 150mm diameter dome showed higher peak loads and was more damage tolerant.
2) Damage mechanisms included matrix cracking, delamination, and fiber pull-out. Delamination absorbed a large percentage of the impact energy.
3) Both dome configurations exhibited non-linear impact behavior, with stiffness reducing and energy dissipation decreasing with accumulated damage from repeated impacts.
Este documento describe los procesos de solidificación que ocurren en las piezas fundidas. Explica que durante la solidificación hay cambios volumétricos, segregaciones y la formación de macro y microestructuras. También describe cómo la estructura de granos depende del sistema de aleación, composición, temperatura de colada y tipo de molde. Finalmente, introduce conceptos como el módulo de enfriamiento y cómo este afecta el orden y velocidad de solidificación.
El documento describe el Análisis del Modo de Falla y sus Efectos (AMFE), una herramienta para identificar y prevenir fallas potenciales. Se desarrolló originalmente para la industria aeroespacial en los años 1970 y desde entonces se ha aplicado a una variedad de industrias. El AMFE involucra un análisis sistemático de un grupo multidisciplinario para detectar fallas potenciales, evaluar sus efectos, y determinar acciones para eliminar o reducir las probabilidades de falla.
Las 5S es una práctica de calidad japonesa para el mantenimiento integral de una empresa que incluye la clasificación y organización de elementos en el lugar de trabajo, limpieza y mantenimiento de la higiene, y compromiso con la disciplina. Aplicar las 5S mejora la calidad, elimina tiempos muertos, reduce costos, aumenta la productividad, crea un mejor ambiente laboral, y genera mayores beneficios para la empresa y sus empleados.
El documento describe la historia de la calidad desde tiempos antiguos, cuando los constructores podían ser ejecutados por fallas en la calidad de las casas. También señala que la calidad total tuvo su origen en Japón y ahora es importante para todas las empresas. Explica que la calidad total debe comunicarse a los trabajadores, proveedores y clientes para que la empresa tenga éxito. Finalmente, destaca que una buena calidad reduce costos y racionaliza recursos.
1. El documento describe la historia de la calidad y el control estadístico desde épocas antiguas hasta el presente. Se destacan las contribuciones de pioneros como Shewart, Deming y Juran.
2. En las primeras etapas, la inspección era la principal estrategia para garantizar la calidad. Con la revolución industrial surgieron los primeros inspectores dedicados a detectar productos defectuosos.
3. En el siglo XX, Shewart introdujo las gráficas de control estadístico y el ciclo PHVA. Los j
Este documento trata sobre la gestión de la calidad. Define calidad como el conjunto de propiedades y características de un producto o servicio que le confieren su aptitud para satisfacer las necesidades del cliente. Explica diferentes modelos de calidad como el control de calidad, la garantía de calidad y la calidad total. Resalta la importancia de identificar las necesidades del cliente y establecer sistemas de gestión de calidad para mejorar continuamente la satisfacción del cliente.
Este documento explica el diagrama de Pareto, incluyendo su historia, definición, cómo se elabora y sus usos. El diagrama de Pareto es una herramienta gráfica que permite identificar los pocos problemas más importantes sobre los cuales concentrar los esfuerzos de mejora. Se basa en el principio de que el 20% de las causas generan el 80% de los efectos. El documento incluye ejemplos de diagramas de Pareto de causas y fenómenos.
Este documento introduce los conceptos fundamentales de la corrosión. Explica que la corrosión puede ser seca o húmeda, y describe varios tipos de corrosión localizada como por picaduras, en resquicios o galvánica. También cubre los costos económicos de la corrosión y métodos para proteger contra la corrosión.
El documento presenta información sobre diferentes temas relacionados con materiales e ingeniería de materiales. Se describen las propiedades y aplicaciones de varios metales y aleaciones como el acero, aleaciones de cobre, plomo, aluminio, magnesio y plata. También se discuten conceptos sobre la estructura cristalina de los metales, tratamientos térmicos, procesos de conformación y clasificación de plásticos.
El documento proporciona información sobre los sistemas integrados de gestión. Explica que un sistema integrado de gestión permite unificar diferentes sistemas de gestión de una organización, como calidad, medio ambiente y seguridad, bajo una sola base documental. Detalla algunos de los beneficios de este enfoque como facilitar la gestión y el mejoramiento continuo. Luego presenta los objetivos del sistema integrado de gestión del INVIMA, que incluyen incrementar competencias, satisfacer al ciudadano y cumplir la legislación.
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2. 2
Lab 2: points of interest
• Consider the following items in the (second) Lab.
• Relate the fracture morphology of wood to what we discussed in this lecture concerning laminated
composites.
• For the wood experiments, see if you can identify a point group that applies to the symmetry of
the properties.
• Compare wood to man-made composites: is it more or less complicated than, say, carbon
reinforced plastics?
• For the steel Lab, try using the Thermocalc results to define which second phases (mainly carbides)
you expect to observe in your heat treated samples.
• Can you detect changes in fracture morphology as a function of test temperature (steels)? Can
you relate the fracture surface features to the measured grain size? What about the spacing of the
pearlite colonies (depending on the microstructure)?
• Can you detect changes in fracture morphology as a function of microstructural change? For
example, in the normalized (pearlitic) condition, can you detect the lamellae at the fracture
surface? Do you think that there is any interaction between the fracture process and the lamellar
structure?
• For the quench+tempered condition, can you relate the particle (carbide) spacing to features on
the fracture surface?
• For the martensitic condition, can you estimate the energy that should be absorbed if it goes only
towards creating crack surface? How does this number compare with a reasonable surface energy
for iron?
• The fracture surfaces of the steel often show features that resemble delamination: what causes
this, and why would you not see them under brittle fracture conditions? Can you relate them to
the banding that you sometimes see in metallography?
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3. 3
Objective
• The objective of this lecture is to show you how to
exploit microstructure in order to maximize toughness,
especially in brittle materials.
• Part of the motivation for this lecture is to explain the
science that supports and informs the second Lab on the
sensitivity of mechanical properties to microstructure.
• Note that the equations used are not derived - rather
the emphasis is on basic principles and a broad range of
methods for toughening.
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4. Questions & Answers
1.Describe 3 ways in which microstructure can be used to
maximize fracture toughness. Lamination, crack bridging
and transformation toughening.
2.Explain what is meant by the “weakest link principle” in
connection with brittle materials. In a brittle materials it
is the largest flaw (aka weakest link) that will open and
cause the material to fail.
3.Explain the terminology used to orient toughness tests.
See the notes. Which orientations will show high
toughness and which low values? For example, weak
planes oriented perpendicular to a crack will divert the
crack and give higher toughness. How does this relate to
laminated composites? See above.
4.Discuss the effect of impurities in steels, for example, on
the trade-off between strength and toughness.
Impurities (e.g. O, N, C, S) in any metal typically have low
solubility and are thus present as ceramic particles.
These particles act as nucleation points for cracks and
voids, which lower toughness (for a given strength).
5.Describe the various extrinsic toughening methods for
brittle materials and the pros and cons of each one. See
the notes for these details.
6.Describe how transformation toughening works. Briefly,
metastable particles transform only when a high tensile
stress near a crack tip is applied to them; the
transformation strain results in extra energy required to
advance a crack. What is the point of adding dopants to
ZrO2 in order to control transformation temperatures?
This controls the degree of metastability. Why is there a
critical size for the particles of ZrO2? Because the
particles only retain their high temperature, metastable
state by being containing in the matrix.
7.How is micro-cracking similar to transformation
toughening, and how does it differ? Similar in that work
is done to crack a particle which contributes to
toughness; obviously differs in the mechanism.
8.How can we estimate the contribution to (or increase in)
toughness from transformation toughening or
microcracking? See notes for an equation involving the
process zone height.
9.How do fibers toughen ceramic matrix composites? By
crack bridging, i.e. the fibers carry load across a crack.
Why is it helpful to toughness if the fibers are not
perfectly bonded to the matrix? Because work has to be
done to pull the fibers out of their matrix.
4
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5. 5
Applications?
Why do we care about toughness?
Courtney
(Ch. 13)
http://ecow.engr.wisc.edu/cgi-bin/get/neep/541/allentodd/notes/
• Steels are used to build pressure vessels for nuclear reactors. The
irradiation that these vessels experience, however, lowers the toughness
of the steels and raises the DBTT (see figures below for Charpy impact
energy versus test temperature). This must be allowed for in the design
and operation of the reactors.
• This, and related issues, is discussed in the course on Materials for
Nuclear Energy Systems, 27-725.
Examinable
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6. 6
Applications: ceramic gas turbines
The thermal efficiency of a gas turbine engine is directly related to its operating temperature.
Conventional gas turbines use Ni-based alloys whose operating temperature is limited by their
melting point (although clever design of thermal barrier coatings and cooling has dramatically
raised their capabilities). Ceramic (oxide) components have much higher melting/softening
points but their intrinsic toughness is far too low. Therefore the toughening of structural
ceramics is essential if these systems are to succeed. The silicon nitride-based part shown (left)
has machined strengths of up to 960 MPa and as-processed strengths of up to 706 MPa.
www.p2pays.org/ref%5C08/07468.pdf -
www1.eere.energy.gov/vehiclesandfuels/pdfs/success/advanced_gas_turbine.pdf
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7. 7
Key Points
• Maximizing fracture resistance requires maximizing work done in
breaking a material.
• Minimize defect content, especially voids, cracks in brittle materials.
• Increasing toughness generally requires adding additional structural
components to a material, either at the microscopic scale or by making a
composite.
• If appropriate (in relation to the way in which a material is loaded),
laminate the material i.e. put in crack deflecting planes.
• If appropriate (in relation to the way in which a material is loaded),
include stiff fibers in the material to give load transfer and fiber pull-out.
• Design the composite to have inclusions that deflect the crack path.
• Design the composite to include particles that transform (or crack) and
thus require work to be done for crack propagation to take place.
Examinable
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8. 8
Strength versus toughness
• If you imagine testing the (tensile) strength of a material
that you could make arbitrarily tough or brittle, how
would its measured strength vary?
Toughness
Breaking Strength
?
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9. 9
Strategies for toughness and
microstructure
• Yield strength depends on the obstacles to
dislocation motion.
• Toughness is more complex: there is no direct
equivalent to obstacles to dislocation motion.
• Instead, we must look for ways to (a) eliminate
or minimize cracks; (b) ways to maximize the
energy cost of propagating a crack.
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10. 10
(a) Minimize or eliminate cracks
• How do we eliminate cracks?
• First, consider the sources of cracks:
- in metals, voids from solidification are deleterious
(especially in fatigue), so minimizing gas content during
solidification helps (Metals Processing!).
- rough surfaces (e.g. from machining) can be made
smooth.
- also in metals, large, poorly bonded (to the matrix)
second phase particles are deleterious, e.g. oxide
particles. Therefore removal of interstitials (O, N, C, S)
from steel melts (or Fe & Si from Al) is important
because they tend to react with the base metal to form
brittle inclusions (as in, e.g. clean steel technology).
Examinable
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11. 11
(a) Minimize or eliminate cracks
• How do we minimize cracks, either number (density) or their
effect?
Grain Structure:
- there are various mechanisms that lead to cracks at grain
boundaries, or at triple junctions between boundaries. Therefore -
in some materials - making the grain size as small as possible is
important because it determines the maximum crack size. Crack
size matters because of stress concentration at the crack tip: longer
cracks mean higher stress concentrations.
- how to minimize grain size? Either by thermomechanical
processing (maximum strain + minimum recrystallization
temperature) or by starting with small powders and consolidating
to 100% density.
Examinable
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12. 12
Distributions
• Remembering that it is the largest crack that limits breaking strength,
it is not the average crack length that matters but rather the
maximum crack size that we should care about.
• For materials in which the grain size determines the typical crack size,
experience shows that the grain size distribution is approximately
constant (and approximately log-normal). The maximum grain size
observed is a small multiple of the average - about 2.5 times.
• Also important in distributions is the spatial distribution of particles
(that can generate cracks); cracks at, or near the surface are more
deleterious than cracks in the interior.
• In brittle materials in particular, it is the largest flaw that determines
the (breaking) strength. Therefore we refer to the weakest link
principle. This in turn means that we must consider extremes values in
the distribution of flaws.
• A useful source of information on extreme values is the on-line NIST
Handbook:
http://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm.
Also search with key words “extreme values strength materials”.
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13. 13
Spatial Distributions
• Anisotropic spatial distributions are most commonly
encountered in thermomechanically processed metals.
They occur, for example, in silicon nitride processed
(tape casting + sintering) to promote directional growth
of beta-Si3N4 for high thermal conductivity heat sink
materials.
• The sensitivity of toughness to the direction in which the
testing is performed has led to a special jargon for
specimen orientation.
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14. 14
Specimen Orientation Code
[Hertzberg]
• The first letter denotes the loading direction; the second letter
denotes the direction in which crack propagation occurs. This is an
example of bi-axial alignment which just means that two directions
have some particular alignment, not just one.
Examinable
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15. 15
Mechanical Fibering
[Hertzberg]
Lowest
toughness
• Any second phase particles present from solidification tend to be elongated and
dispersed in sheets parallel to the rolling plane; called “stringers”. Such stringers are
commonly found in (older) aerospace aluminum alloys.
• Toughness in the S-L or S-T orientations is typically much lower than for the L-T or L-
S orientations because the crack plane is parallel to the planes on which the particles
lie close to one another.
• Charpy tests on steels (Lab 2, for example) often show delaminations for L-S or T-S
oriented tests.
Examinable
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16. 16
Inclusion effects
• Graph plots variation in
strength with (plane strain)
toughness with varying sulfur
contents in 0.45C-Ni-Cr-Mo
steels.
• Increasing levels of S lead to
lower toughness at the same
strength level.
• This occurs because the sulfur
is present as sulfide inclusions
in the steel.
• “Clean steel” technologies for
steel making have reduced
this problem in recent years.
[Dieter]
Examinable
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17. 17
Laminate Composites
[Hertzberg]
• The weakness of such layers of inclusions, which provide planes on which crack
nucleation is relatively easy, can however be exploited.
• By providing planes of low crack resistance perpendicular to the anticipated crack
propagation direction, a crack can be deflected, thereby reducing the load at the
crack tip and increasing the work that must be done in order to advance the crack tip.
• In designing a laminate composite, it is important to balance the fracture toughness
(brittleness) against the interfacial weakness. The more brittle the matrix (layers), the
weaker the interfaces between the layers need to be. Example: Wood, Mollusc shells
SiC-fiber reinforced Cu.
Web: femas-ca.eu,
via images.google
Examinable
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18. 18
Effect of lamination on the DBTT
• The effect of orienting the laminations of a composite in
the crack arrestor configuration is to dramatically lower
the transition temperature.
• This is actually an example of crack deflection.
[Hertzberg, after Embury]
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19. 19
Explanation of Lamination
This crack propagation
direction leads to
delamination and crack
blunting (more toughness)
This crack propagation
direction follows the
inclusion+grain shape
(less toughness)
[Hertzberg]
Examinable
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20. 20
Energy absorption: 1
• How do we increase the amount of energy consumed in
propagating a crack?
- One method, already discussed, is to maximize the amount of
plastic work. This requires the yield strength to be minimized so as
to maximize the size of the plastic zone.
- For very tough materials, however, it turns out that the same
parameters that control ductility also affect toughness. Lower
densities of second phase particle increase toughness. Second
phase particles well bonded to the matrix increase toughness.
Small differences in thermal expansion coefficient help (Why?).
• Read papers by Prof. Warren Garrison’s group.
Examinable
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21. 21
Energy absorption: 2
• Other methods of toughening materials are generally called
extrinsic. There are three general classes of approach:
1) Crack deflection (and meandering)
2) Zone shielding
3) Contact shielding
• The term “shielding” means that the crack tip is shielded from some
part of the applied stress.
• Up to this point, the discussion has been mostly about metal-based
materials which are intrinsically tough to being with (except at low
temperatures). Extrinsic toughening methods are mostly
concerned with ceramics in which the intrinsic toughness is low.
Examinable
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22. 22
Energy absorption: 3
• Sub-divisions of extrinsic toughening methods:
1) Crack deflection (and meandering)
2) Zone shielding
- 2A Transformation Toughening
- 2B Microcrack toughening
- 2C Void formation
3) Contact shielding
- 3A Wedging/ crack bridging
- 3B Ligament/fiber bridging
- 3C Crack sliding, interference
- 3D Plasticity induced crack closure
Examinable
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23. 23
1 Crack deflection
• If particles of a second phase are present, large differences in
elastic modulus can either attract or repel the crack.
• Some authors (e.g. Green) distinguish between crack bowing and
crack deflection. Technically, the former is toughening from
deflection in the plane of the crack and the latter is deflection out
of the plane of the crack.
• In either case, the net result is that the crack tip no longer sees as
large a stress as it would if the crack were straight, and in the
plane.
• Crack deflection can be caused by particles that are more resistant
to cracking, or have different elastic stiffness (higher or lower
modulus).
• Laminate composites also achieve crack deflection, as previously
discussed.
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25. 25
Zone Shielding: 2A transformation
toughening
• Various mechanisms exist for shielding crack tips from some of
the applied (and concentrated) stress.
• The best known mechanism is transformation toughening.
• This applies to both metals (stainless steels, Hadfield steels) and
ceramics (zirconia additions).
• The principle on which the toughening is based is that of
including a phase that is metastable at the service temperature
and which will transform when loaded (but not otherwise).
• The transformation always has a volume change associated with
the change in crystal structure, which can be written as a strain.
The product of stress and strain is then the work done or
expended during the (stress-induced) transformation.
Examinable
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26. 26
2A Transformation toughening:
transformation strain
• The large volume change on transformation is equivalent
to a significant transformation strain which is the key to
the success of the method. Recall that our basic measure
of fracture resistance is the work done, ∫ d, in breaking
the material.
• The volume change (d) is ~ 4 %, accompanied by a shear
strain of ~ 7 %. Since the transformation has a particular
habit plane (i.e. a crystallographic plane in each phase in
common), two twin-related variants occur in each
particle so that the shear strains are (approximately)
canceled out. This leaves only the 4 % dilatational
(volume) strain that contributes to the work done.
Examinable
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27. 27
2A Transformation toughening:
phase change in zirconia
• The classic example of transformation toughening is the addition of a
few (volume) % of ZrO2 to oxides and other brittle ceramics.
• The highest temperature form of zirconia is cubic (c-ZrO2) with an
intermediate tetragonal form (t-ZrO2). Both of these have significantly
larger atomic volumes than the low temperature, monoclinic form (m-
ZrO2), and the cubic has a larger volume than the tetragonal form.
• In order to reduce the driving force for the tetragonal monoclinic
transformation (i.e. lower the transformation temperature), some
“stabilizer” is added. Typical are ceria (Ce2O3) and yttria (Y2O3).
• The subtle point about this approach is that some “trick” is needed in
order to keep the zirconia from transforming once the material is cooled
to room temperature, i.e. to maintain it in a metastable, untransformed
state.
• The following slides show phase relationships for ZrO2 with CaO, and
ZrO2 with Y2O3.
Examinable
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28. ZrO2 and CaZrO2
• In pure ZrO2 there is a large
volume change for the
tetragonal to monoclinic
transition upon cooling, starting
at about 1150 °C.
• This leads to cracking
throughout a ZrO2 component
and thus total mechanical
failure.
• This is avoided by doping with Calcia
from 3-7 % to form cubic and
monoclinic (and no tetragonal about
1000 °C).
• Below this T diffusion is too slow to
form enough monoclinic to generate
the unwanted cracks.
• “Partially Stabilized Zirconia”
28
Slide courtesy Dr. Alpay, Univ. Connecticut: http://www.ims.uconn.edu/~alpay/Group_Page/Courses/MMAT%20244/Lecture%2005.ppt
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29. Yttria Stabilized Zirconia
• The monoclinic transition
can be suppressed even
further by stabilizing
zirconia with yttria from
3-8 %.
• Retains cubic and
tetragonal phases
(avoiding monoclinic)
down to roughly 700 °C.
• Yttria, partially, and cubic
stablized zirconia (CZ) are
commercially useful.
29
Slide courtesy Dr. Alpay, Univ. Connecticut: http://www.ims.uconn.edu/~alpay/Group_Page/Courses/MMAT%20244/Lecture%2005.ppt
Examinable
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30. 30
2A Transformation toughening:
critical size of zirconia particles
• An important consequence of the volume change on transformation is that it leads to an elastic driving
force that opposes the transformation for particles embedded in a matrix of a different material.
• The size effect is, however, quite subtle. If we were to consider only the elastic energy from the
volume change then this would be proportional to the (volumetric) driving force for the phase change.
In fact, however, there is a shear strain associated with the phase transformation that is larger than the
dilatational strain. This shear strain is accommodated by having multiple shear variants, whose
average shear strain is close to zero, leaving only the volume change. These variants have interfaces
(boundaries) between them, which requires the creation of surface area in the transformation.
Therefore there is, in fact, a balance between the release of volumetric driving force (offset by the
dilatational strain energy) and the creation of internal interfaces between martensite variants.
• Therefore we take advantage of having the zirconia embedded as small particles in the matrix of the
ceramic to be toughened.
• The particles must be small enough for the elastic energy term to be effective. The upper limit in
particle size for retention of the high temperature (tetragonal) phase is ~ 0.5 µm.
[Green]
Examinable
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31. 31
2A Transformation toughening:
transformation work
• Consider the effect of the tensile stress in the vicinity of the crack tip: the stress
removes the constraint on each particle, allowing it to transform. The
transformed particle was metastable, thermodynamically, and so remains in the
low T, monoclinic form after the crack has gone by.
• The stress acting to cause the transformation strain performs work and so
energy is consumed in the phase transformation. This energy (work done) adds
to the surface energy required to create crack length.
• Additional toughening arises from the particles causing crack deflection.
Examinable
http://www.vertebr.ae/B
log/wp-
content/uploads/2010/0
2/zirconia-
transformation-
toughening-in-
ceramics.gif
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32. 32
2A Transformation toughening:
the process zone
• The region in which transformation occurs becomes the
crack wake as the crack propagates. The region around the
crack tip is known as the process zone because this is where
the toughening process is operative.
[Green]
Crack propagation direction
Process zone width
Examinable
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33. 33
2A Transformation toughening:
microstructure
• Microstructural evidence for the
transformation is obtainable
through x-ray diffraction and
Raman spectroscopy (the two
different forms of zirconia have
quite different infra-red
spectra).
• (a) lenticular particles of MgO-
stabilized ZrO2 (untransformed)
in cubic ZrO2.
(b) transformed particles of ZrO2
around a crack (dashed line).
[Chiang]
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34. 34
2A Transformation
toughening: limits on toughening
• As the particle size is increased,
so the particles become less and
less stable; the transformation
becomes easier and more
effective at toughening the
material. If the particles become
too large, however, the
toughening is lost because the
particles are no longer stabilized
in their high temperature form.
• Effect of test temperature?
• Effect of stabilizing additions to
the ZrO2?
[Green]
Examinable
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35. 35
2A Transformation
toughening: quantitative approach
• It is not possible to lay out the details of how to describe transformation
toughening in a fully quantitative fashion here.
• An equation that describes the toughening effect is as follows, where K
is the increment in toughness (units of stress intensity, MPa√m):
∆K = C E Vtrans trans h / (1-n)
C is a constant (of order 1), E = elastic modulus,
Vtrans = volume fraction transformed,
trans = transformation strain (dilatation, i.e. bulk expansion),
h is the width of the process zone, and
n is Poisson’s ratio.
• What controls the width of the process zone?
Examinable
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36. 36
2B Microcracking
• Less effective than transformation toughening is
microcracking in the process zone.
• Microstructural elements are included that crack over
limited distances and only at the elevated (tensile)
stresses present in the crack tip.
[Green]
Examinable
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37. 37
2B Microcracking
• The principle of Micro-cracking as a toughening mechanism is that one designs
the material so that additional (micro-)cracking occurs in the vicinity of the crack
tip as it advances, thereby increasing the crack area created (per unit advance of
crack), thereby increasing the toughness (resistance to crack propagation).
• This is most effective in two-phase ceramics in which the 2 phases have different
CTEs. As the material cools after sintering (or other high temperature
processing), one phase is in tension (and the other in compression, to balance).
The phase under residual tensile stress will crack more easily than the other one
under additional tensile load, e.g. near a crack tip.
• Now we have to consider what can happen in the material. If the residual stress
is too high, then the phase in tension will crack during cooling. If it is entirely
(micro-)cracked, then no further cracking can occur at a crack tip (to absorb
energy) and the toughening effect is lost. What controls this, however, is the
grain size: smaller grain sizes are more resistant to cracking. To find the critical
grain size, dc, we use the Griffith equation, with Kco as the fracture toughness and
R as the residual stress, substituting grain size for crack size:
dc = ( Kco / R )2
• The process zone size, rc, then depends on the ratio of the actual grain size, d, to
the critical grain size:
• The graph, from Courtney, shows how one needs to be within a certain rather
narrow range of grain size in order to have a finite process zone size and
therefore effective toughening. Grain sizes larger than the critical grain size
simply result in spontaneous cracking. Too small grain sizes (< 0.6 dc) mean no
micro-cracking at the crack tip.
rc
d
»
0.232
1-
d
dc
æ
è
ç
ö
ø
÷
2
[Courtney]
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38. 38
2B Microcracking: particles
• Microcracking depends on second phase particles that can crack easily.
• The cracking tendency depends on particle size (typically, 1µm): if they are too small, then the stress
intensity does not reach their critical Kc, based on the Griffith equation.
• (Tensile) residual stresses aid cracking, so differences in thermal expansion (with the matrix) are
important. Recall that the thermal expansion, as a (stress-free) strain, is equal to the Coefficient of
Thermal Expansion (CTE or a) multiplied by the change in temperature (∆T), thermal = a ∆T. Where a
volumetric strain is important,
V0+∆V = (l0 + ∆l)3 = { l0 (1+thermal) }3 = l0
3 (1+3+32+3) V0 (1+3thermal) ; ∆V/V = 3thermal
• An equation that describes the toughening effect is as follows, where ∆K is again the increment in
toughness (units of stress intensity):
∆K = C Vf E crack h / (1-n)
C is a constant (of order 1),
E = modulus,
crack = cracking strain (dilatation),
h is the width of the process zone, and
n is Poisson’s ratio. The cracking strain is approximately 3*strain associated with the difference in CTE:
crack 3∆a ∆T.
• Note the strong similarity to the equation that describes transformation toughening! The only
difference is the physical meaning of the strain term. If the volume fraction, Vf, is not given, one can
assume =1, if there are nearly equal fractions of the two phases so that most grains crack.
• See the next slide for an explanation of how the cracking strain is equivalent to an eigenstrain.
Examinable
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40. 40
2C Void formation
• Void formation in a process zone can have a similar
effect to micro-cracking. In materials such as high
strength steels, e.g. 4340, the source of the voiding is
ductile tearing on a small scale as the crack opens.
• The spatial organization of the voids is important.
Random distributions are better than either clusters or
sheets. Carbide particles in steels, or dispersoid
particles in aluminum alloys (e.g. Al3Fe) are typical
nucleation sites for voids. Sheet-like sets of voids can
arise from carbide particles that have grown on
martensite or bainite laths during tempering of
martensitic microstructures.
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41. 41
3A Crack wedging/ bridging
• Wherever the crack results in interlocking grain shapes
exerting force across the crack, stress (intensity) at the
crack tip is reduced.
[Chiang]
Crack
opening
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42. 42
3B Fiber/ligament bridging (Composites)
• Anything that results in a load bearing link across the crack (behind the tip)
decreases the stress (intensity) at the crack tip.
• Either rigid (elastic) fibers (ceramic matrix composites) or plastic particles
(ductile metal particles in an elastic matrix) are effective.
• In order to estimate the increase in toughness, one can calculate a work
associated with crack advance and then estimate with
∆K = (EG).
[Chiang]
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43. 43
3B Fiber/ligament bridging
• Scanning electron micrographs of a SiC whisker bridging
at various stages of crack opening. From left to right,
the stress intensity is increasing.
[Green]
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44. 44
3B Fiber/ligament bridging
strain dependence
• The balance between
fiber strength, matrix
strength and the
fiber/matrix interface
is critical.
• In general, a relatively
weak fiber/matrix
interface promotes
toughness.
• Why? [Green]
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45. 45
3D Plasticity induced crack closure
• Plasticity induced crack closure is another
way of stating the effect of plastic
deformation around the crack tip.
• Very tough materials exhibit an interesting
behavior in Charpy impacts. For high
ductilities, the specimen can deform
without fully breaking, with consequent
enormous energies absorbed.
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46. 46
References
• D.J. Green (1998). An Introduction to the Mechanical Properties of
Ceramics, Cambridge Univ. Press, NY.
• Materials Principles & Practice, Butterworth Heinemann, Edited by C.
Newey & G. Weaver.
• G.E. Dieter (1986), Mechanical Metallurgy, McGrawHill, 3rd Ed.
• Courtney, T. H. (2000). Mechanical Behavior of Materials. Boston,
McGraw-Hill.
• R.W. Hertzberg (1976), Deformation and Fracture Mechanics of
Engineering Materials, Wiley.
• N.E. Dowling (1998), Mechanical Behavior of Materials, Prentice Hall.
• Y.-T. Chiang, D.P. Birnie III, W.D. Kingery, Physical Ceramics (1997), Wiley,
New York, ISBN 0-471-59873-9.
• A.H. Cottrell (1964), The Mechanical Properties of Matter, Wiley, NY.
• For gas turbine engines, ASME runs a yearly conference called ASME
Turbo Expo, which has sessions that discuss materials issues.
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