This document summarizes Griffith and Irwin fracture mechanics theories. [1] Griffith's theory explains brittle fracture and proposes that crack growth occurs when the potential energy released by fracturing exceeds the new surface energy. [2] Irwin modified Griffith's theory for ductile materials by including a term for the energy dissipated by plastic deformation near the crack tip. Irwin's theory partitions the energy into stored elastic energy driving fracture and dissipated energy resisting it. Crack growth occurs when the stored energy exceeds the dissipated energy.
fracture mechanics and damage tolerance .Why do high strain rate, low temperature and triaxial state of stress promote brittle fracture?Method of Crack/Crack Like Defect Analysis
Mumbai University.
Mechanical Engineering
SEM III
Material Technology
Module 2.2
Fatigue Failure:
Definition of fatigue and significance of cyclic stress, Mechanism of fatigue and theories of fatigue failure, Fatigue testing, Test data presentation and statistical evolution, S-N Curve and its interpretation, Influence of important factors on fatigue, Notch effect, surface effect, Effect of pre-stressing, corrosion fatigue, Thermal fatigue.
This PPT discusses Fatigue and Fracture mechanism, some history and problems. It has included on research paper. You can refer the literature review for further study of the topic.
This presentation is for mechanical engineering/ civil engineering students to help them understand the different type of destructive mechanical testing of materials. The tensile testing, hardness, impact test procedures are explained in detail.
Engineering Fracture Mechanics. Engineers try to have high-strength, high ductility, high crack resistance, and faultless structures. The most reliable approach is "No cracks - no problems,"
When all is not possible, there are different methods of prevention of catastrophic failure: increase crack resistance by ductile material, by local heating; decrease SIF by placing holes on the crack path, by patching, by stiffing elements or by using composite materials. "Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure vessels. It is better to allow a semi-elliptical crack to grow through the wall and to detect it by leaking than to have the dynamic start and failure of the whole vessel. There are two characteristics of the material: crack resistance for semi-elliptical crack and crack resistance for through crack.
fracture mechanics and damage tolerance .Why do high strain rate, low temperature and triaxial state of stress promote brittle fracture?Method of Crack/Crack Like Defect Analysis
Mumbai University.
Mechanical Engineering
SEM III
Material Technology
Module 2.2
Fatigue Failure:
Definition of fatigue and significance of cyclic stress, Mechanism of fatigue and theories of fatigue failure, Fatigue testing, Test data presentation and statistical evolution, S-N Curve and its interpretation, Influence of important factors on fatigue, Notch effect, surface effect, Effect of pre-stressing, corrosion fatigue, Thermal fatigue.
This PPT discusses Fatigue and Fracture mechanism, some history and problems. It has included on research paper. You can refer the literature review for further study of the topic.
This presentation is for mechanical engineering/ civil engineering students to help them understand the different type of destructive mechanical testing of materials. The tensile testing, hardness, impact test procedures are explained in detail.
Engineering Fracture Mechanics. Engineers try to have high-strength, high ductility, high crack resistance, and faultless structures. The most reliable approach is "No cracks - no problems,"
When all is not possible, there are different methods of prevention of catastrophic failure: increase crack resistance by ductile material, by local heating; decrease SIF by placing holes on the crack path, by patching, by stiffing elements or by using composite materials. "Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure vessels. It is better to allow a semi-elliptical crack to grow through the wall and to detect it by leaking than to have the dynamic start and failure of the whole vessel. There are two characteristics of the material: crack resistance for semi-elliptical crack and crack resistance for through crack.
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Fracture means the end of life of any structure. The immobilization or the structure could be obviated through detailed study of the environment, fabrication methods and sequences used, as well as the mechanical properties of the materials.
This is known as fracture mechanics.
This part of the lecture will deal with meaning of fracture in ductile and brittle materials under various conditions of loading following load opening of adefect, crack like inherited during fabrication processes.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
2. Introduction
Fracture mechanics is the field of mechanics concerned with the study of the propagation of
cracks in materials.
a) Mode I fracture – Opening mode (a tensile stress
normal to the plane of the crack),
b) Mode II fracture – Sliding mode (a shear stress acting
parallel to the plane of the
crack and perpendicular to the crack front), &
c) Mode III fracture – Tearing mode (a shear stress acting
parallel to the plane of the crack m
and parallel to the crack front).
There are three ways of applying a force to enable a crack to
propagate:
Source:Fracture Toughness Determinations by Means of
Indentation Fracture (Book) By Enrique Rocha-Rangel
3. Fracture Modes
• Classification is based on the ability of material to experience plastic deformation.
• Ductile fracture
Accompanied by significant plastic deformation
• Brittle fracture
Little or no plastic deformation
Sudden, Catastrophic
4. Griffith Criterion
• Explains the failure of brittle materials.
Motivation
The stress needed to fracture bulk glass is around 100 MPa.
The theoretical stress needed for breaking atomic bonds of glass is approximately 10,000 Mpa.
Theory
Experiments on glass fibers suggested that the fracture stress increases
as the fibre diameter decreases due to the presence of microscopic flaws
in the bulk materials.
Source : DTD Handbook Section 2.2.6.1.1.
5. Experiment
Griffith introduced an artificial flaw in his experimental glass specimen.
Experiment showed that the product of the square root of the flaw length (a) and the stress at fracture (σf) was
nearly constant, which is expressed by the equation:
Contradiction
Linear elasticity theory predicts that stress (and hence the strain) at the tip of a sharp flaw in a
linear elastic material is infinite.
6. Griffith Energy Balance
• The energy approach states that crack extension (i.e., fracture) occurs when the energy available for crack growth is
sufficient to overcome the resistance of the material.
• The material resistance may include the surface energy, plastic work, or other types of energy dissipation associated
with a propagating crack.
According to the first law of thermodynamics, when a system goes from a non-equilibrium state to equilibrium, there is a
net decrease in energy-
• A crack can form (or an existing crack can grow) only if the process causes the total energy to decrease or remain
constant.
• Thus the critical conditions for fracture can be defined as the point where crack growth occurs under equilibrium
conditions, with no net change in total energy.
7. • Consider a plate subjected to a constant stress σ which contains a
crack 2a long .
Assumption:
a) Plate width>>2a and
b) Plane stress conditions.
For the crack to increase-
Sufficient potential energy must be available in the plate to overcome
the surface energy of the material.
Fig.1. Cracked specimen
8. The Griffith energy balance for an incremental increase in the crack area dA, under equilibrium conditions, can be
expressed in the following way:
For the cracked plate illustrated in Fig.1, Griffith used the stress analysis of Inglis [3] to show that
Since the formation of a crack requires the creation of two surfaces, Ws is given by
γs=Surface energy of the material contd.
Where
E = total energy
Π= potential energy supplied by the internal strain energy
and external force
Ws= work required to create new surfaces
Πo= potential energy of an uncracked plate and
B = plate thickness.
10. Irwin Theory or Modified Griffith theory
Motivation
For ductile materials such as steel although the relation still holds, the surface energy (γ) predicted by
Griffith's theory is usually unrealistically high.
Theory
In ductile materials (and even in materials that appear to be brittle), a plastic zone develops at the tip of the crack.
As the applied load increases, the plastic zone increases in size until the crack grows and the elastically strained
material behind the crack tip unloads.
The plastic loading and unloading cycle near the crack tip leads to the dissipation of energy as heat. Hence, a
dissipative term has to be added to the energy balance relation devised by Griffith for brittle materials.
11. Irwin’s strategy was to partition the energy into two parts:
a) The stored elastic strain energy which is released as a crack grows. This is the thermodynamic driving force for
fracture.
b) The dissipated energy which includes plastic dissipation and the surface energy (and any other dissipative forces
that may be at work). The dissipated energy provides the thermodynamic resistance to fracture. Then the total
energy is
γ = surface energy and
Gp = plastic dissipation (and dissipation from other sources)
per unit area of crack growth.
The modified version of Griffith's energy criterion can then be written as
Source: Wikiwand Fracture mechanics
12. References
1. Griffith, A. A. (1921), "The phenomena of rupture and flow in solids" , Philosophical Transactions of the
Royal Society of London, A, 221: 163–198.
2. Irwin G (1957), Analysis of stresses and strains near the end of a crack traversing a plate, Journal of
Applied Mechanics 24, 361–364.
3. Inglis, C.E., “Stresses in a Plate Due to the Presence of Cracks and Sharp Corners.” Transactions of the
Institute of Naval Architects, Vol. 55, 1913, pp. 219–241.
4. T.L. Anderson (1995). Fracture Mechanics: Fundamentals and Applications. CR Press. ISBN 970849316562.