This document discusses techniques for determining the spatial and size distributions of spherical inclusions in mild steel. Planar measurements taken from electropolished surfaces are compared to measurements taken from fracture surfaces. It is found that the average dimple size on fracture surfaces is always greater than the most probable first neighbor spacing from planar measurements. Additionally, the mean inclusion size is smaller on fracture surfaces compared to electropolished surfaces. These differences are believed to arise from the fracture process itself.
The present investigation deals with the static analysis of adhesively bonded inner tapered double lap joint in laminated FRP composites subjected to transverse loading using three-dimensional theory of elasticity based finite element method. Many researchers studied the influences of various parameters on the failure behaviour on the composites. In those studies, the typical bonding parameters are surface conditions, fillet, bond line thickness, and environmental conditions. In the present study the stresses and deformation characteristics of adhesively bonded inner tapered double lap joint made of generally and especially orthotropic laminates (FRP) subjected to transverse loading for the three different adhesive angles, three different adhesive thicknesses with different fibre angle orientations, i.e. the adhesive angles from 350 to 450 increased in steps of 50. The variation in stresses and deflection are studied when the fibre angle orientation is varied from 00 to 900 in steps of 150. The adhesive thickness varies from 0.05 to 0.15 insteps of 0.05mm. In all the above cases stresses and displacements at various locations are evaluated for the static boundary conditions
Structural Changes in the Surface Layer of Deep Rolled Samples Due to Thermal...IJERA Editor
Deep rolling processes initiate plastic deformations in the surface layer. The local characteristics of deformation are dependent on the induced stress expressed by the local stress tensor. Equivalent stresses above yield strength cause plastic deformation. Additionally the intrinsic energy, e. g. the dislocation density, is enhanced and the residual stress state is changed. The effects to a deep rolled surface from an increase in temperature are mainly dependent on the material, the microstructure, the initial residual stress state, the inclusion density, the distribution of soluted alloying elements and the plastic deformation. In the described experiments the interactions between deformation and temperature of the steel grade AISI 4140 (42 CrMo 4) used for all further experiments in a transregional Collaborative Research Center (CRC) were to be examined. The most simple investigation methods were chosen deliberately to allow a better statistical support of correlations between introduced strains and material reactions for a wide variation of process parameters. Since the visual effects by light microscopy in AISI 4140 were very small, the experiments were repeated with german grade 18 CrNiMo 7-6 (comparable to AISI 4820). This paper focuses on the micro structural changes in defined deep rolled surface regions due to an increase in temperature. The work described is part of the Collaborative Research Center “Process Signatures”, collaboration between Bremen University, Technical University Aachen, Germany and Oklahoma State University Stillwater, USA.
The present investigation deals with the static analysis of adhesively bonded inner tapered double lap joint in laminated FRP composites subjected to transverse loading using three-dimensional theory of elasticity based finite element method. Many researchers studied the influences of various parameters on the failure behaviour on the composites. In those studies, the typical bonding parameters are surface conditions, fillet, bond line thickness, and environmental conditions. In the present study the stresses and deformation characteristics of adhesively bonded inner tapered double lap joint made of generally and especially orthotropic laminates (FRP) subjected to transverse loading for the three different adhesive angles, three different adhesive thicknesses with different fibre angle orientations, i.e. the adhesive angles from 350 to 450 increased in steps of 50. The variation in stresses and deflection are studied when the fibre angle orientation is varied from 00 to 900 in steps of 150. The adhesive thickness varies from 0.05 to 0.15 insteps of 0.05mm. In all the above cases stresses and displacements at various locations are evaluated for the static boundary conditions
Structural Changes in the Surface Layer of Deep Rolled Samples Due to Thermal...IJERA Editor
Deep rolling processes initiate plastic deformations in the surface layer. The local characteristics of deformation are dependent on the induced stress expressed by the local stress tensor. Equivalent stresses above yield strength cause plastic deformation. Additionally the intrinsic energy, e. g. the dislocation density, is enhanced and the residual stress state is changed. The effects to a deep rolled surface from an increase in temperature are mainly dependent on the material, the microstructure, the initial residual stress state, the inclusion density, the distribution of soluted alloying elements and the plastic deformation. In the described experiments the interactions between deformation and temperature of the steel grade AISI 4140 (42 CrMo 4) used for all further experiments in a transregional Collaborative Research Center (CRC) were to be examined. The most simple investigation methods were chosen deliberately to allow a better statistical support of correlations between introduced strains and material reactions for a wide variation of process parameters. Since the visual effects by light microscopy in AISI 4140 were very small, the experiments were repeated with german grade 18 CrNiMo 7-6 (comparable to AISI 4820). This paper focuses on the micro structural changes in defined deep rolled surface regions due to an increase in temperature. The work described is part of the Collaborative Research Center “Process Signatures”, collaboration between Bremen University, Technical University Aachen, Germany and Oklahoma State University Stillwater, USA.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Numerical Investigation on the Stability of an Underground Mine Opening in ...Premier Publishers
The stability of an underground opening is an essential factor in the mine operation; the proper prediction of the stability is mandatory for the optimum support design and smooth mine operation. Previous researchers have identified the presence of pre-existing natural fractures as a critical factor for the stability of subsurface opening. However, the variation of natural fracture impact due to different fracture parameter value is yet to be identified. Fracture intensity, orientation, and opening are the most dominant parameters that determine the magnitude of the impact on stability. This study has built an underground mine tunnel model using Itasca’s software 3DEC and analysed the sensitivity of the aforementioned essential parameters. Moreover, the built model has been analysed for varying fracture density, orientation, scaling exponent and distribution and the corresponding displacements of the tunnel in different directions are simulated. The outcome of this study is helpful for the prediction of the mine opening stability and the optimization of support system design.
Modified maximum tangential stress criterion for fracture behavior of zirconi...dentalid
The veneering porcelain sintered on zirconia is widely used in dental prostheses, but
repeated mechanical loadings may cause a fracture such as edge chipping or delamination.
In order to predict the crack initiation angle and fracture toughness of zirconia/veneer bilayered
components subjected to mixed mode loadings, the accuracy of a new and
traditional fracture criteria are investigated. A modified maximum tangential stress
criterion considering the effect of T-stress and critical distance theory is introduced, and
compared to three traditional fracture criteria. Comparisons to the recently published
fracture test data show that the traditional fracture criteria are not able to properly predict
the fracture initiation conditions in zirconia/veneer bi-material joints. The modified
maximum tangential stress criterion provides more accurate predictions of the experimental
results than the traditional fracture criteria
When a ductile material with a crack is loaded in
tension, the deformation energy builds up around the crack tip
and it is understood that at a certain critical condition voids are
formed ahead of the crack tip. The crack extension occurs by
coalescence of voids with the crack tip. The “characteristic
distance” (Lc) defined as the distance b/w the crack tip & the void
responsible for eventual coalescence with the crack tip. Nucleation
of these voids is generally associated with the presence of second
phase particles or grain boundaries in the vicinity of the crack tip.
Although approximate, Lc assumes a special significance since it
links the fracture toughness to the microscopic mechanism
considered responsible for ductile fracture. The knowledge of the
“characteristic distance” is also crucial for designing the size of
mesh in the finite element simulations of material crack growth
using damage mechanics principles. There is not much work
(experimental as well as numerical) available in the literature
related to the dependency of “characteristic distance” on the
fracture specimen geometry. The present research work is an
attempt to understand numerically, the geometry dependency of
“characteristic distance” using three-dimensional FEM analysis.
The variation of “characteristic distance” parameter due to the
change of temperature across the fracture specimen thickness was
also studied. The work also studied the variation of “characteristic
distance”, due to the change in fracture specimen thickness.
Finally, the ASTM requirement of fracture specimen thickness
criteria is evaluated for the “characteristic distance” fracture
parameter. “Characteristic distance” is found to vary across the
fracture specimen thickness. It is dependent on fracture specimen
thickness and it converges after a specified thickness of fracture
specimen. “Characteristic distance” value is also dependent on the
temperature of ductile material. In Armco iron material, it is
found to decrease with the increase in temperature.
LABORATORY MODEL TESTS TO EFFECT OF DENSITY TO FILL MATERIAL ON THE PERFORMAN...IAEME Publication
The effective functioning of reinforced earth structures is very much dependent on the quality of materials and construction. Many times, due to poor quality of the materials used and poor quality control measures exercised, the density of the reinforced soil fill is not up to the design requirements, leading to underperformance or distress of the reinforced soil walls. Therefore, it becomes necessary to evaluate the level of underperformance vis-à-vis that of relative compaction. In view of this, in the present study, a series of laboratory experiments were carried out on a model soil wall of 300 mm high with vertical face, prepared at different density states of 95%, 80% and 70% of MDD of IS HCT. The wall was subjected to monotonic load applied through a model square footing of size (B) equal to 50 mm on the surface at an offset distance of 1(B). Similar tests were carried out on the soil wall reinforced with a Woven Geotextile in wrap around form; to study the effect of density on the performance of reinforced soil wall. The results indicated proportionality between relative compaction level and performance of soil wall without and with reinforcement.
Numerical Study of Star Anchor Plate Embedded in Cohesive SoilIJERA Editor
Indonesia as an archipelago country has a very long coastline about 90.000 kms. Specifically for shore and offshore, there are many buildings utilizing structures including floating deck, mooring dolphin, offshore platforms etc. Those requires a solution to maintain the stability of the structures due to the vertical movement of tides and horizontal movement of currents, wind and waves. To maintain the stability due to buoyant force, structure of anchors are needed. Various types of the anchor have been widely used such as drag, helical, anchor plate circular shape and square. This study aims to do the development of new modifications of a plate anchor type star with 4 leaves with an area of a fixed and diameter equivalent different on any variations. Ultimate pullout capacity was obtained by using numerical geomechanics analysis within finite difference method. A perfectly plastic soil model was used with a tresca yield criterion. Results are presented including break-out factors based on various anchor shapes and embedment depth. Our findings are also compared with previous numerical and empirical solutions.
Experimental Determination of Fracture Energy by RILEM Methodtheijes
This paper deals with investigation of fracture energy (GF) of concrete. The study involves experimental determination of fracture energy (GF) by testing three point bend concrete beams of same size but varying notch to depth ratios. RILEM fracture energy (GF) and Stress Intensity factor values is determined
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Dynamic Analysis of Double-Skin Composite Steel PlatesIOSR Journals
Double Skin Composite (DSC) plates are subjected to impact required to cause complete perforation and the accompanied failure modes are investigated. The amount of energy absorbed is calculated by capturing the residual velocity of penetrator after perforating the lower plate. The difference in initial kinetic energy and residual kinetic energy is the amount of energy absorbed by the panel. In the present paper a non-linear three-dimensional finite element models for Double Skin Composite panels subjected to dynamic loading is introduced. Pilot model is used to investigate the failure pattern in the composite panel when subjected to impact loads by rigid steel penetrator, while the other models are used to analyze the energy absorption capacity of such system when perforated. Results showed that such elements have good ability of absorbing energy when subjected to perforation, due to ductility of lower plate skin and vertical stiffness of lower shear studs.
A Review of Masonry Buckling CharacteristicsIJERA Editor
Masonry load bearing wall subjected to vertical concentric and eccentric loading may collapse through instability. In this Paper the buckling behaviour of masonry load bearing wall of different slenderness ratio were investigated by many researcher has been reviewed via testing a series of scale masonry wall subjected to concentric and eccentric vertical loading. It is also observed that buckling behaviour is greatly influenced by the material properties of units, mortar and units-mortar interface. The influence of nonlinear behaviour of interface element, slenderness ratio and various end conditions have been investigated together with the effect of different end eccentricity of vertical load
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Numerical Investigation on the Stability of an Underground Mine Opening in ...Premier Publishers
The stability of an underground opening is an essential factor in the mine operation; the proper prediction of the stability is mandatory for the optimum support design and smooth mine operation. Previous researchers have identified the presence of pre-existing natural fractures as a critical factor for the stability of subsurface opening. However, the variation of natural fracture impact due to different fracture parameter value is yet to be identified. Fracture intensity, orientation, and opening are the most dominant parameters that determine the magnitude of the impact on stability. This study has built an underground mine tunnel model using Itasca’s software 3DEC and analysed the sensitivity of the aforementioned essential parameters. Moreover, the built model has been analysed for varying fracture density, orientation, scaling exponent and distribution and the corresponding displacements of the tunnel in different directions are simulated. The outcome of this study is helpful for the prediction of the mine opening stability and the optimization of support system design.
Modified maximum tangential stress criterion for fracture behavior of zirconi...dentalid
The veneering porcelain sintered on zirconia is widely used in dental prostheses, but
repeated mechanical loadings may cause a fracture such as edge chipping or delamination.
In order to predict the crack initiation angle and fracture toughness of zirconia/veneer bilayered
components subjected to mixed mode loadings, the accuracy of a new and
traditional fracture criteria are investigated. A modified maximum tangential stress
criterion considering the effect of T-stress and critical distance theory is introduced, and
compared to three traditional fracture criteria. Comparisons to the recently published
fracture test data show that the traditional fracture criteria are not able to properly predict
the fracture initiation conditions in zirconia/veneer bi-material joints. The modified
maximum tangential stress criterion provides more accurate predictions of the experimental
results than the traditional fracture criteria
When a ductile material with a crack is loaded in
tension, the deformation energy builds up around the crack tip
and it is understood that at a certain critical condition voids are
formed ahead of the crack tip. The crack extension occurs by
coalescence of voids with the crack tip. The “characteristic
distance” (Lc) defined as the distance b/w the crack tip & the void
responsible for eventual coalescence with the crack tip. Nucleation
of these voids is generally associated with the presence of second
phase particles or grain boundaries in the vicinity of the crack tip.
Although approximate, Lc assumes a special significance since it
links the fracture toughness to the microscopic mechanism
considered responsible for ductile fracture. The knowledge of the
“characteristic distance” is also crucial for designing the size of
mesh in the finite element simulations of material crack growth
using damage mechanics principles. There is not much work
(experimental as well as numerical) available in the literature
related to the dependency of “characteristic distance” on the
fracture specimen geometry. The present research work is an
attempt to understand numerically, the geometry dependency of
“characteristic distance” using three-dimensional FEM analysis.
The variation of “characteristic distance” parameter due to the
change of temperature across the fracture specimen thickness was
also studied. The work also studied the variation of “characteristic
distance”, due to the change in fracture specimen thickness.
Finally, the ASTM requirement of fracture specimen thickness
criteria is evaluated for the “characteristic distance” fracture
parameter. “Characteristic distance” is found to vary across the
fracture specimen thickness. It is dependent on fracture specimen
thickness and it converges after a specified thickness of fracture
specimen. “Characteristic distance” value is also dependent on the
temperature of ductile material. In Armco iron material, it is
found to decrease with the increase in temperature.
LABORATORY MODEL TESTS TO EFFECT OF DENSITY TO FILL MATERIAL ON THE PERFORMAN...IAEME Publication
The effective functioning of reinforced earth structures is very much dependent on the quality of materials and construction. Many times, due to poor quality of the materials used and poor quality control measures exercised, the density of the reinforced soil fill is not up to the design requirements, leading to underperformance or distress of the reinforced soil walls. Therefore, it becomes necessary to evaluate the level of underperformance vis-à-vis that of relative compaction. In view of this, in the present study, a series of laboratory experiments were carried out on a model soil wall of 300 mm high with vertical face, prepared at different density states of 95%, 80% and 70% of MDD of IS HCT. The wall was subjected to monotonic load applied through a model square footing of size (B) equal to 50 mm on the surface at an offset distance of 1(B). Similar tests were carried out on the soil wall reinforced with a Woven Geotextile in wrap around form; to study the effect of density on the performance of reinforced soil wall. The results indicated proportionality between relative compaction level and performance of soil wall without and with reinforcement.
Numerical Study of Star Anchor Plate Embedded in Cohesive SoilIJERA Editor
Indonesia as an archipelago country has a very long coastline about 90.000 kms. Specifically for shore and offshore, there are many buildings utilizing structures including floating deck, mooring dolphin, offshore platforms etc. Those requires a solution to maintain the stability of the structures due to the vertical movement of tides and horizontal movement of currents, wind and waves. To maintain the stability due to buoyant force, structure of anchors are needed. Various types of the anchor have been widely used such as drag, helical, anchor plate circular shape and square. This study aims to do the development of new modifications of a plate anchor type star with 4 leaves with an area of a fixed and diameter equivalent different on any variations. Ultimate pullout capacity was obtained by using numerical geomechanics analysis within finite difference method. A perfectly plastic soil model was used with a tresca yield criterion. Results are presented including break-out factors based on various anchor shapes and embedment depth. Our findings are also compared with previous numerical and empirical solutions.
Experimental Determination of Fracture Energy by RILEM Methodtheijes
This paper deals with investigation of fracture energy (GF) of concrete. The study involves experimental determination of fracture energy (GF) by testing three point bend concrete beams of same size but varying notch to depth ratios. RILEM fracture energy (GF) and Stress Intensity factor values is determined
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Dynamic Analysis of Double-Skin Composite Steel PlatesIOSR Journals
Double Skin Composite (DSC) plates are subjected to impact required to cause complete perforation and the accompanied failure modes are investigated. The amount of energy absorbed is calculated by capturing the residual velocity of penetrator after perforating the lower plate. The difference in initial kinetic energy and residual kinetic energy is the amount of energy absorbed by the panel. In the present paper a non-linear three-dimensional finite element models for Double Skin Composite panels subjected to dynamic loading is introduced. Pilot model is used to investigate the failure pattern in the composite panel when subjected to impact loads by rigid steel penetrator, while the other models are used to analyze the energy absorption capacity of such system when perforated. Results showed that such elements have good ability of absorbing energy when subjected to perforation, due to ductility of lower plate skin and vertical stiffness of lower shear studs.
A Review of Masonry Buckling CharacteristicsIJERA Editor
Masonry load bearing wall subjected to vertical concentric and eccentric loading may collapse through instability. In this Paper the buckling behaviour of masonry load bearing wall of different slenderness ratio were investigated by many researcher has been reviewed via testing a series of scale masonry wall subjected to concentric and eccentric vertical loading. It is also observed that buckling behaviour is greatly influenced by the material properties of units, mortar and units-mortar interface. The influence of nonlinear behaviour of interface element, slenderness ratio and various end conditions have been investigated together with the effect of different end eccentricity of vertical load
El maquillaje de moda de la primavera, Teatro openair, Aperitivo Cinzano, un nuevo restaurante especializado en tacos de pescado, nuevas tendencias foodie, la vuelta de las noches del Anti-Karaoke...
Comparative Study on Anchorage in Reinforced Concrete Using Codes of Practice...IJERA Editor
The evaluations of anchorage strength of bars in reinforced concrete are varied in codes of practice and
equations by researchers on the base of their approaches and philosophies.
This paper (Part I) aims to have a comparative study between the predictions by codes of practice of BS8110
and EC2 and those equations by Darwin et al, Morita and Fuji, Batayneh and Nielsen and results of 164 tests
from literature.
In this part the case of straight anchorage bars without transverse pressure is considered. Some major parameters
including compressive strength, and in terms of ratio of concrete cover to bar diameter and ratio of anchorage
length to bar diameter , are addressed in detail.
Although various parameters are involved in anchorage design equations, it is observed that every code has
merit over the other codes in some aspect. The presented discussion highlights the major areas of differences
which need attentions in the future for more investigations.
The main conclusion has been presented in part II to include the study of straight anchorages with transverse
pressure. The conclusions should cover the both cases to obtain the fair assessments for bond strength by those
expressions used in this study.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This paper addresses the fracture toughness ( ), or also known as critical stress intensity Factor, according to
conditions of Lineal Elastic Fracture Mechanics (LEFM). The characterization of the mechanical properties in
tensile and fracture toughness of structural steel pipes API-5L used in hydrocarbons transportation was
performed. For fracture toughness, the material was tested through fatigue crack propagation on standardized
compact specimen (CT) according to ASTM E-399 norm. A thickness (B) equal to and a crack size (a) equal
to 0.5w were used. With the porpoise of establishing the adequate conditions at the crack tip, the specimens were
subjected to fatigue pre-cracking by application of repeated cycles of load in tensile-tensile and constant load
amplitude with a load ratio of R = 0.1. The experimental Compliance method was used based on data obtained
from load vs. Crack Mouth Opening Displacement (CMOD). The results show a Stress Intensity factor of 35.88
MPa√m for a 25 mm crack size specimen. The device used for testing is a MTS-810 machine with capacity of
100KN and 6 kHz sampling rate, which meets the conditions of the ASTM E-399 standard. The cracking
susceptibility of steel is influenced by the size, morphology and distribution of non-metallic inclusions,
thermochemical interaction with the environment and microstructure.
We study the link between the indentation size effect and the density of geometrically necessary dislocations (GNDs) through the following
approach: four indents of different depth and hardness were placed in a Cu single crystal using a conical indenter with a spherical tip. The
deformation-induced lattice rotations below the indents were monitored via a three-dimensional electron backscattering diffraction method
with a step size of 50 nm. From these data we calculated the first-order gradients of strain and the GND densities below the indents. This
approach allowed us to quantify both the mechanical parameters (depth, hardness) and the lattice defects (GNDs) that are believed to be
responsible for the indentation size effect.Wefind that theGNDdensity does not increase with decreasing indentation depth but rather drops
instead.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
INTERFACIAL STRESS ANALYSIS OF EXTERNALLY PLATED RC BEAMSIjripublishers Ijri
has become a popular retrofit method due to its rapid, simple and other advantages. However, debonding along the
Steel-RC beam interface can lead to premature failure of the structures. The interfacial stresses play a significant role
in understanding this premature debonding failure of such repaired structures. This paper presents a careful finite
element investigation into interfacial stresses in the adhesive layer bonding RC beam and soffit plate. Finite element
modelling issues like proper selection of contact between adherents and symmetry conditions are first
discussed, with particular attention on appropriate finite element meshes for the accurate determination of interfacial
stresses. The interfacial stress behaviour at plate end has been analysed for two cases of loading taken one by applying
uniformly distributed load and the other with a two point loading. Two special cases are considered in two point
loading – for the cases when the plate terminates with-in the constant moment region (CMR) and for the case when
plate is extended beyond constant moment region where bending moment is minimal. The interfacial stresses are
increasing with a reduction in adhesive layer thickness where as the stresses are increasing with the increase in soffit
plate thickness. Carbon fibre reinforced polymer (CFRP) has shown a significant reduction in interfacial stresses
when compared to steel plate. The interfacial stresses for the plate restricted within the constant moment region are very
high near the plate end leading to flexural debonding compared to the case where plate is extended beyond constant
moment region where bending moment is minimal. The concentration of stresses in the adhesive layer near the plate
end explained the significance in considering their influence in flexural debonding.
INTERFACIAL STRESS ANALYSIS OF EXTERNALLY PLATED RC BEAMSIjripublishers Ijri
Strengthening reinforced concrete (RC) beams by bonding steel or fibre reinforced polymer (FRP) on its tension face
has become a popular retrofit method due to its rapid, simple and other advantages. However, debonding along the
Steel-RC beam interface can lead to premature failure of the structures. The interfacial stresses play a significant role
in understanding this premature debonding failure of such repaired structures. This paper presents a careful finite
element investigation into interfacial stresses in the adhesive layer bonding RC beam and soffit plate. Finite element
modelling issues like proper selection of contact between adherents and symmetry conditions are first
discussed, with particular attention on appropriate finite element meshes for the accurate determination of interfacial
stresses. The interfacial stress behaviour at plate end has been analysed for two cases of loading taken one by applying
uniformly distributed load and the other with a two point loading. Two special cases are considered in two point
loading – for the cases when the plate terminates with-in the constant moment region (CMR) and for the case when
plate is extended beyond constant moment region where bending moment is minimal. The interfacial stresses are
increasing with a reduction in adhesive layer thickness where as the stresses are increasing with the increase in soffit
plate thickness. Carbon fibre reinforced polymer (CFRP) has shown a significant reduction in interfacial stresses
when compared to steel plate. The interfacial stresses for the plate restricted within the constant moment region are very
high near the plate end leading to flexural debonding compared to the case where plate is extended beyond constant
moment region where bending moment is minimal. The concentration of stresses in the adhesive layer near the plate
end explained the significance in considering their influence in flexural debonding.
Keywords-- Interfacial stresses, flexural debonding, constant moment region, soffit plate, finite element method.
Experimental and Analytical Investigation of Drilling of Sandwich Composites:...IOSR Journals
A composite material is made out of a mixture or a combination of two or more distinctly differing
materials which are insoluble in each other and differ in form or chemical composition. The technological and
commercial interest in composite material lies in their superior properties of strength-to-weight, stiffness-toweight,
fatigue and thermal expansion compared to metals. Extensive use of composite in application such as
rockets, satellites, missiles, light combat aircraft, advanced light helicopter and trainer air craft has shown that
India is on par with the advanced countries in the development and use of composites in this area.
Drilling is probably the most important conventional mechanical process and it is the most widely used
machining operation. Prediction of cutting forces for any set of cutting parameters is essential in optimal design
and manufacturing of products. It has been predicted that most of the problem associated with hole making
operation, such as drilling, can be attributed to the force generated during cutting operation. Many
developments and experiments are going on drilling of Sandwich composite for damage free drilling along with
the quality of the hole and the effect of tool geometry and tool material.
This paper aims at the comprehensive analytical and experimental investigation work done on the
composites material. The conclusion of the paper discusses the development and outlines the trends for the
research in this field.
How Carbon Nanotubes Collapse on Different Ag Surface?ijrap
The collapse and stability of carbon nanotubes (CNTs) on noble metal silver different surfaces were studied
using molecular mechanics and molecular dynamics simulations. From the results, it can be seen that the
CNTs can collapse spontaneously onto different silver surface [(1 0 0), (1 1 0), (1 1 1)] due to the van der
Waals force between them. Furthermore, the CNT collapsing on (1 0 0) and (1 1 1) surface are much easier
than that on (1 1 0) surface. Moreover, the results show that the collapsed CNTs exhibit as linked graphene
ribbons and have the largest area to contact with the Ag surface, which greatly enhances adhesion between
the CNTs and the Ag surface and keeps the system much more stable.
How Carbon Nanotubes Collapse on Different Ag Surface? ijrap
The collapse and stability of carbon nanotubes (CNTs) on noble metal silver different surfaces were studied
using molecular mechanics and molecular dynamics simulations. From the results, it can be seen that the
CNTs can collapse spontaneously onto different silver surface [(1 0 0), (1 1 0), (1 1 1)] due to the van der
Waals force between them. Furthermore, the CNT collapsing on (1 0 0) and (1 1 1) surface are much easier
than that on (1 1 0) surface. Moreover, the results show that the collapsed CNTs exhibit as linked graphene
ribbons and have the largest area to contact with the Ag surface, which greatly enhances adhesion between
the CNTs and the Ag surface and keeps the system much more stable.
Vibrational Analysis Of Cracked Rod Having Circumferential Crack IDES Editor
The frequency ratio of torsional vibration of a rod without crack and of rod with crack subjected to torque at the free end for various crack depth and varying crack location is investigated. It is found that even a cracked of small depth is
dangerous at the fixed end, also as the crack depth is increases more than 50% of diameter of rod there is a considerable drop in natural frequency of the rod .
We conducted molecular dynamics simulations to investigate the atomistic edge crack vacancy interactions in graphene. We demonstrate that the crack tip stress field of an existing crack in graphene can be effectively tailored (reduced by over 50% or increased by over 70%) by the strategic placement of atomic vacancies of varied shapes, locations, and orientations near its tip. The crack vacancy interactions result in a remarkable improvement (over 65%) in the fracture strength of graphene. Moreover, at reduced stiffness of graphene, due to a distribution of atomic vacancies, a drastic difference (~60%) was observed between the fracture strengths of two principal crack configurations (i.e. armchair and zigzag). Our numerical simulations provide a remarkable insight into the applicability of the well-established continuum models of crack microdefect interactions for the corresponding atomic scale problems. Furthermore, we demonstrate that the presence of atomic vacancies in close proximity to the crack tip leads to a multiple stage crack growth and, more interestingly, the propagating cracks can be completely healed even under a significantly high applied tensile stress level (~5 GPa). Our numerical experiments offer a substantial contribution to the existing literature on the fracture behavior of two dimensional nanomaterials.
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The background fracture studies leading up to Fractal fracture discovery
PARTICLE SIZE DISTRIBUTIONS AND
INTERPARTICLE SPACINGS IN 2.XX
DIMENSIONAL SPACE
INCLUSIONS ARE A REALITY!!
Results were used to improve welding practice
(in general) and to develop the welding practice
used on the atomic submarines
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15?~"'DS-~'~ 12/pf8J
2. II 0.52 0.47 0.37
42 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES
PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 43
this is not the case when considering a particle sampled from the volume. Tables
5 and 6 show a comparison between planar, corrected volume, and fracture
surface measurements. The agreement is not perfect although the corrections do
tend to correct the planar measurements in the direction of the fracture surface
measurements.
TABLE 5-Comparisons between two-dimensional mean diameters, corrected
three-dimensional mean diameters [6], and fracture surface mean diameters.
and fracture surfaces for the three different cases. The plots are shown as
cumulative log normal probability plots. In all cases investigated in this study,
the frequency distributions were skewed, asymmetric, and yielded the best linear
plots when the cumulative frequency distribution was plotted on log normal
probability paper. It is felt that the distributions are, therefore, all log normal
and will be considered as such in the following discussions. Table 4 shows a
TABLE 4-Summary of particle size distribution statistics obtained from extraction replicas.
Specimen
II 0.17 0.15 0.20
A. Electropolished -Planar
Specimen XA1 (µm) XG1 (µm) UA1 (µm) 1n2 uG1
0.64 0.58 0.28 0.20
II 0.52 0.50 0.17 0.11
III 0.38 0.36 0.12 0.11
B. Fracture Surfaces-Room Temperature
XAF (µm) X"GF (µm) uAF (µm) 1n2 uGF
0.53 0.47 0.27 0.26
II 0.37 0.32 0.20 0.29
III 0.36 0.32 0.18 0.23
0.64 0.53 0.53
III 0.38 0.34 0.36
TABLE 6-Comparisons between two-dimensional arithmetic standard deviation,
corrected three-dimensional arithmetic standard deviation,
and fracture surface arithmetic mean diameter.
Specimen
0.28 0.24 0.27
III 0.12 0.11 0.18
~
It is felt that only fair agreement between the corrected values and measured
values is obtained due to the fact that the probability of observing a particle on a
fracture surface depends upon the mechanism of particle-nucleated void
formation. Both particle fracture and interface decohesion occur during the void
nucleation step. Thus, the probability of observing a particle on a fracture
surface most likely depends upon both the diameter and the surface area of the
particle.
summary of the statistical data obtained for all the distributions which were
studied. The arithmetic mean and the arithmetic standard deviation were
computed in the standard manner from the dat~. The geometric mean and
standard deviation were calculated from 3 ~
Discussion
In2uG = (::) 2
InXG = InXA -0.5 In2 uG (5)
In each case it was found that the arithmetic mean diameter of the particle
found on a fracture surface was smaller than that found on a planar surface. As
discussed by Ashby and Ebling [6], the diameter of a particle as measured on a
surface extraction replica is not the same as the true mean diameter of the
particle for the volume. The difference arises from the fact that probability of
intersecting a particle in a planar section is proportional to its diameter whereas
(4)
Spatial Distribution and Dimple Size
The combined set of measurements (that is, determination of spatial
randomness of the nearest-neighbor interparticle spacing distribution and
measurement of the mean linear dimple intercept size) constitutes a method by
3 Ashby and Ebling's [6] nomenclature is used here.
3. D. E. Passoja! and D. CHill!
Comparison of Inclusion Distributions
on Fractu re Su rfaces and in the Bu Ik
of Carbon-Manganese Weldments
REFERENCE: Passoja, D. E. and Hill, D. C., "Comparison of Inclusion Distributions
on Fracture Surfaces and in the Bulk of Carbon-Manganese Weldments," Fractog-
raphy-Microscopic Cracking Processes, ASTM STP 600, American Society for
Testing and Materials, 1976, pp. 30--46.
ABSTRACf: Techniques are developed for determining the spatial and size
distributions of spherical inclusions in mild steel. The relations between these
distributions as found on electropolished surfaces and as found on fracture surfaces
are determined. It is shown that the first neighbor spatial distributions on
electropolished surfaces can be described analytically. The average dimple size on a
fracture surface is always greater than the most probable first neighbor spacing. The
inclusion size distributions both on electropolished and fracture surfaces are shown
to be log-normal. The mean inclusion size on a fracture surface is always smaller than
that on an electropolished surface. These variations are believed to arise from the
nature of the fracture process.
KEY WORDS: fractography, inclusions, crack propagation, fractures (materials),
fracture properties, carbon steels, geometric surfaces, weld metal, weldments, particle
size distribution, particle density (concentration)
Nomenclature
tv Volume fraction of inclusions
n Number of events
r First neighbor separation
r* Most probable first neighbor separation
r Average first neighbor separation
XA
Arithmetic mean
XG Geometric mean
!AI Arithmetic one-dimensional mean (after Ashby and Ebling [6])
!A2 Arithmetic two-dimensional mean (after Ashby and Ebling)
!AF Arithmetic fracture surface mean
XGF
Geometric fracture surface mean
D Dimple size (equal to 1.5 [)
Ds Average particle spacing (after Kocks [8])
K1c
Fracture toughness
I Research scientist, Central Scientific Laboratory, and research supervisor, Linde
Research Department, respectively, Union Carbide Corporation, Tarrytown, N. Y. 10591.
30
PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 31
L
Ns
Pen)
Per)
µ
a
aAI
aA2
aAF
aGF
Mean linear intercept dimple size
Average planar inclusion density
Probability as a function of n
Probability as a function of r
Number of elements in system-average number of
Standard deviation
Arithmetic one-dimensional standard deviation
Arithmetic two-dimensional standard deviation
Arithmetic standard deviation on fracture surface
Geometric standard deviation on fracture surface
There is considerable evidence to indicate that the fracture toughness of
metals is related in some Why to a characteristic feature of the microstructure.
The feature is thought to be related fundamentally to the fracture process itself,
that is, to play a determinant role in the progression of the fracture.
Considerations of the physical characteristics of the microstructure usually
precede the development of a more specific fracture model and use of such a
model to explain fracture behavior in any system.
Several investigators have recognized salient microstructural features and have
related them to fracture toughness. Using Krafft's [1] 2 tensile ligament
instability theory, Birkle, Wei, and Pellisier [2] measured the spacing between
sulfide particles on extraction replicas and were able to relate the fracture
toughness to the spacing between the particles. Hahn and Rosenfield [3]
considered several factors which influenced the toughness of aluminum alloys
which included:
I. the extent of the heavily strained region in front of the crack tip,
2. the size of the strained ligaments-which was related to the volume fraction
of cracked particles, and
3. the work required to rupture the ligaments.
They furthermore recognized that both the size, distribution, and particle type
influenced the fracture process. By plotting K1c
versus tv -! /6 ifv being the
volume fraction of cracked particles), the authors were able to develop
convincing arguments that fracture toughness in several different material.s could
be related to inclusions. In his work on high strength steels, Yoder [4] found a
somewhat coarser spacing on fracture surfaces which correlated with fracture
toughness. Furthermore, fractographs published in his work clearly indicate that
the spacing which correlated was considerably larger than the dimple size.
In order to determine more definitively the relationship between features
found on fracture surfaces, and those of the microstructure, and to quantify the
existence and nature of such differences, we performed experiments to compare
the features of fracture surfaces with those of plane-polished surfaces in three
ferrous materials. In light of the findings just ;eferenced, we chose to use a
2 The italic· numbers in brackets refer to the list of references appended to this paper.
4. 46 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES
The second moment can be written as
(II)
So that
(I2)
References
[1]
[2]
[3]
Krafft, J. M.,Applied Materials Research, VoL 3, 1964, p. 88.
Birkle, A. J., Wei, R. P., and Pellissier, G. E., Transactions, American Society for
Metals, VoL 59, 1966, p. 98L
Hahn, G. T. and Rosenfield, A. R., 5th Spring Meeting of the Metallurgical Society
of the American Institute of Mining, Metallurgical, and Petroleum Engineer's, 29
May to 1 June 1973.
Yoder, G. R., Metallurgical Transactions, Vol. 3, 1972, p. 185 L
Hill, D. C. and Passoja, D. E., Welding Journal, VoL 53, 1974, p. 481-s.
Ashby, M. F. and Ebeling, R., Transactions, Metallurgical Society of the American
Institute of Mining, Metallurgical, and Petroleum Engineers, VoL 236, 1966, p.
l396.
Hilliard, J. E., Metal Progress, Vol. 85, 1964, p. 99.
Kocks, U. F., Philosophical Magazine, VoL 13, 1966, p. 541.
[4]
[5J
[6]
[7]
[8]
(
6. 34 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES
•
0{]
0
0
0 •
0
~
'" ". '"
:;: Sl ~
".
..,
.:.-~
H
~-t!
'" ~ ~ '" '" '" ~ Sl ~
".
.., "'. '"~~
PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 35
'.
A
>-
• <" ...• . . ,
.
.
:
. .
' ..
I'
. ..
"
...
.
•
.
M<,"
G
A
. •
.~ ..
.,.
. "'. •
.
",
.
t
~.
•
..... . .
~.
, ..
•
.
- ..
B
FIG. 2-111ustrative example of concentric circle measuring technique. (A) shows a tracing
of the unetched, polished metallographic section shown in (B). Five concentric circles are
shown superimposed on a particle marked as A on the micrograph. The magnitude of the
vector R is shown in (A); original magnification, x]OOO.
Appendix II. The agreement between the computed values and measured values
is fairly good considering that only 200 distances were measured on each sample.
It is important to note, however, that the computed curve shape is similar to the
measured values in each case, and that the trends (that is, decreasing values) are
the same for both the computed and measured values. It would appear the
discrepancies between the computed and measured values arise from either a loss
7. PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 37 36 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES
.0.1
;
Comparison of Computed
and
Measured lnferpor lie Ie
r--
Distribution Spac i n 9 s
)
ill
r-- Opticol- EJectropolished
-
r-!!...
• •;
'--
• •)
•
•;
• r-
•i--
Il· .
.0.2.0
r.oj
I
PI,'
C.'
Comparison of Computed
r- and
Measured interparticle
5 Distribution Spacings
I--
I
• • Optical Electropolished
• •1--....-
.0
fT - •
..... ~.;
• --, -
•• ~
IT
• • .Ial_ .. - - .d
1..0 2.0 3.0 4.0
r(lIm) ..
5..0 6.0 7..0 B.C
.0.25
0.21
rPltl
1..0 2.0 3[)
r(pm) - )'
4..0 S.C 6[) 7..0 B.C
.0.05
.0..0
FIG. 3-Frequency distribution for planar first nearest-neighbor interparticle spacing, Steel 1.
t
Comparison of Computed
and
r---- Measured Interparticle
Distribution Spacing
,
IT..-
• ITr.- Optical - Electropalished
I-a-'---
)
• •
... •it--
•
• •~.I
•
0.20
G_ 5-Frequency distribution for planar first nearest-neighbor interparticle spacing, Steel
measured_ It is well known that, during ductile fracture, voids usually
leate on inclusions, grow, and link-up to form the fracture surface_
lsurements of the dimple size should, therefore, be related to the interparticle
~ing, in some manner, but should be complicated by the fracture surface
metry_ We attempted to demonstrate this in the following manner.
tereo photomicrographs were taken randomly from ten different areas on
ldard Charpy specimens fractured at room temperature_ In each instance, a
Ipled fracture surface was present. three lO-cm circles were located on each"
eomicrograph pair. When viewed in the stereo viewer the circles merged and
y three circles appeared to be located over the fracture surface. The
rsections between the circles and the dimples were marked off and the
[section rules outlined by Hillard [7] for measuring grain sizes were followed
lustrated in Fig. 6. Table 2 shows a summary of the measured values .
.s in the nearest-neighbor planar interparticle measurements, Table 1, the
Ids exhibited in Table 2 are similar, but in every case the mean-linear-dimple
rcept size is greater than the nearest-neighbor planar interparticle spacing.
differences between the measured distances can be explained in the
owing manner: dimples are created during the void link-up stage upon final
lration of the fracture surface. The fracture surface is created as a result of
I nucleation and growth in a volume of material near the crack tip. For this
on the spacings between the dimple forming voids do not necessarily
'espond to the most probable value of a single nearest-neighbor interparticle
;ing, but rather it depends upon a number of factors such as the local stress
0.15
P(r)
0.1
0.0
1.0 2.0 ~O 4~
r0m) •
11.0 6.0 7.0 8.0
FIG. 4-Frequency distribution for planar first nearest-neighbor interparticle spacing, Steel
II.
of particles during the extraction step or arise from counting only 200 (a limited
number of) nearest neighbor distances with the concentric circle method.
Dimple Size Measurements
In order to compare the planar nearest-neighbor interparticle spacing with
some meaningful fracture surface feature, the mean linear dimple intercept size
8. PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 39
38 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES
"0
<J)
';
I ~ ": «:0-
E
0
~IU
~
0
"0
~
I
<J)
....
I ~i5l q ~'t;
'"
N
'" <J)
>:>.
~<00
~
.l:
"-
'">:>.
"-
~ "0
,S <J)
"- ';
I ~ M
"!0 0-
M
"'" E M N
..:::: 0
,~
~ U
"2 E
<00 ~
~ 1"-
%l "0
~ <J)
"
::;
I 0 .-. '<:t
..:::: '" N N....
'"<J)
"-
~,0.....,
<00
".2!
'""'1:l
" "0
"- <J)
::;
';<00
I ~ '"' q%l 0-
E E N N N
'1:l
0
~ U~
~'"'1:l
~
"::; "-
>:>. "0
E "....
0 i5l
I N 0 "!
" '"
N N
~ <J)
" ~
"
'--- I t
""'"~0
FIG. 6-( A) shows polished, etched section of the typical microstructure observed in ,'="
'""-
'" ,~
teels I through III; original magnification, xl 000. (B) shows one photo of a stereo pair >:>.
'0..
'ith two circles used to measure the dimple size, Intersections between the dimples and the E .......
" '" '" t"-
O '" J::t:: 0 0 0
I ,..., ,..., ,...,'rcles are marked on the micrograph; original magnification, x3250, I E <:: x x x,..., u 0
~ ~ N
'"' 00
w u 0 ,..., ,...,
....l <: ;'! .,., r..:
Ild the particle size distribution. Dimples are thus some irregular shape, such as
I
a:l ;;:<C
f-< :.:.J
11 n sided polygon, when viewed as a planar projection in the SEM.
Kocks [8] has shown that in some instances the average distance between a
article and its two or three neighbors is more a meaningful distance than the
c
earest-neighbor distance. This distance can be calculated by <J)
E
'u I - = -D = 1 18 N -1/2
<J)
(3) 0-
s . s u:>
9. 40 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES
PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 41
TABLE 2-Summary of mean linear dimple intercept measurements.
7-Comparison of log normal cumulative probability plot of particle diameters for
nd fracture surface for Steels f through fl!.
InclU$lon [)oomeler
Cl.rnulolive Probob,hly
I
([>lrocllonRephcosJ
,
.,
..,
.6
.,
••
•• O~ 0
• 0
• 0
• 0
• 0
eEleclropOI,shed
o• DRoam Temperoture
Chorpy
Cumulohve ProbabIlIty
'~r'------------------------,
.,
6
,
Inclusion Dio'7'lller
Cumulative PrObability
IT
(E.'roction Replicas)
,.,.8
.'.6
• C
• 0
• 0
• 0
o
o
o
o eElecl'opollshod
o Room Temperalur,
Chorpy
.I' 0 I
0.01 10 20 JC) 40 50 60 10 00 90 95 99 999
Cumuloli". Probablhty
Cumuklilve Probablhty
m
(hlroct_Repllcas)
! '(5.9
~~~, 6
~ 5
,.
..
:JAoom Tlln'lpe.olure
Cho'P)'
.11 ' , I
01.1 10 20 30 405060 70 80 90 95 99 ~99
C.."....,lal,ve ProbabIliTy
L(µm)Specimen a(µm)
3.3 0.65
2.6II 0.48
2.5III 0.19
Table 3 shows a comparison between measured D (equal to 1.5 L) and Ds as
calculated by Kocks equation. Thus, it can be seen that the number of nearest
neighbors is important when considering the mean linear intercept dimple size
measurement. There is only fair agreement between Ds and the measured values
due to a number of contributory factors such as:
I. the statistical scatter due to the topographical features (non-planarity),
2. the physical aspects of the fracture process resulting in a physically
meaningful standard deviation, and
3. local differences in the number of nearest neighbors-the most common
number projected in a plane appears to be five.
TABLE 3-Comparisons between measured dimple sizes and computed spacings.
Specimen D (µm)
4.95.0
3.9 4.4II
III 3.7 3.4
Particle Size Distribution
Direct carbon extraction replicas were made of fracture surfaces and
electropolished surfaces taken ~0.5 cm away and parallel td' the fracture surfase.
One thousand particles which could uniquely be associated with dimples were
measured on the fracture surface replicas from each specimen. One thousand
particles were measured on the planar cut and electropolished surfaces from each
specimen. Mechanical polishing was tried, but gave inconsistent results with too
few particles and unreaJistically large mean sizes. Following Ashby and Ebling's
[6] particle extraction efficiency arguments, our assumptions were that the
particle extraction efficienoy was not 100 percent but there was equal
probability of extracting a particle over the entire size range (that is, particle
extraction was not selective).
Figure 7 shows cumulative probability plots of particles extracted from planar
10. PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 45 44 FRACTOGRAPHY-MICROSCOPIC CRACKING PROCESSES
(7)
(8)
which planar surface features can be compared in a meaningful manner with
fracture surface features. Successful application of these methods to our
problem required that two criteria be met.
1. The fracture mode must be related to particle nucleated microvoids.
2. The center-to-center spatial distribution must be random. (This can be and
was checked by means of the Poisson test.)
Differences between planar surface features and fracture surface features can
best be understood by considering the topographical differences which exist
between a fracture surface and a planar surface. The mean linear dimple
intercept, for example, is larger than the most probable planar nearest-neighbor
interparticle spacing due to the fact that voids grow around inclusions and link
up in a volume of material in front of the crack tip. A single planar,
nearest-neighbor interparticle spacing, therefore, does not describe the dimple
formation process since the volume distribution of nearest neighbors is a more
relevant description of the fracture process. For this reason Kocks' correction
appears to bring agreement between planar and fracture surface features.
~PPENDIX I
¥eldment Preparation
Three weldments were made in ASIS baseplate using an E70S-3 electrode4 by
he GMA process according to American Welding Society Standard AS. 18-69.
.11 welding was done in the flat position using automatic equipment. The
IOminal welding conditions were: current, 200 A; voltage, 27 V; and travel
peed, 30 em/min. The shielding gas composition was varied to provide different
)xidizing potentials and different levels of inclusions in the weldments. The
.hielding gases used and weld identifications are: CO2, I; Ar-25% CO2, II; and
r-2% O2, III. Weld compositions are given in Table 7.
TABLE 7 - Weldmetal compositions.
ield Designation c Mn Si o
0.08 0.45 0.12 0.099
II 0.09 0.78 0.32 0.044
III 0.08 1.00 0.46 0.042 Particle Size Distributions
Inclusions which are present in the bulk are the same set of inclusions which
cooperatively participate in fracture and form the fracture surface. The
differences which are observed between inclusion sizes found on a planar surface
and on a fracture surface are believed to result both from the geometrical
differences involved in planar versus volume sampling and from the fracture
process.
.PPENDIX II
ipatial Distribution Function
Equation 2a represents the incremental number of inclusions surrounding a
ingle inclusion in a thin strip of width /::;.r:
/::;.Ns = rrrNs exp (-r2 Ns) /::;.r (6)
lhe exponential term represents the probability that the distance between any
wo inclusions lies between rand r + /::;.r. The distribution can be normalized by
:hanging Eq 6 into a continuous distribution, equating the integrand to I, and
olving for the normalization constant, k:
Conclusions
I = kJ~rrNs r exp (- Nsr2) dr
k= ~
rr
Techniques have been developed for quantifying and comparing both the
spatial and size distributions of inclusions on fracture surfaces and in the bulk. A
nearest-neighbor interparticle spacing distribution function of the form
(2b)
4 All terms in this section refer to the American Welding Society designations.
apparently describes a random planar spatial distribution of particles for the
three ferrous materials used in this study.
A correction must be made for two or more nearest neighbors in order to
bring agreement between dimple size measurements performed on a fracture
surface and particle density measurements performed on planar surfaces.
Particle size measurements indicate that the particle sizes are log normally
distributed both on planar surfaces and fracture surfaces. Differences between
the two distributions can be rationalized by considering the details of the
particle sampling process during fracture.
,0 that
¢ (r) = 2Ns r exp (-Nsr2) (9)
~quation 9 is the continuous distribution function from which various moments
)f r can be calculated. For instance, the average value of r is
'----
r=.r: r¢(r)dr= 1/2 J 1T (10)
Ns
11. I = kJ~ 7TNs r exp (- Nsr2) dr
k = .2
7T
(7)
(8)
PASSOJA AND HILL ON INCLUSION DISTRIBUTIONS 45
APPENDIX I
Weldment Preparation
Three weldments were made in AS IS baseplate using an E70S-3 electrode4 by
the GMA process according to American Welding Society Standard AS. 18-69.
All welding was done in the flat position using automatic equipment. The
nominal welding conditions were: current, 200 A; voltage, 27 V; and travel
speed, 30 cm/min. The shielding gas composition was varied to provide different
oxidizing potentials and different levels of inclusions in the weldments. The
shielding gases used and weld identifications are: CO2, I; Ar-2S% CO2, II; and
Ar-2% O2, III. Weld compositions are given in Table 7.
TABLE 7-Weldmetal compositions.
Weld Designation c Mn Si o
0.08 0.45 0.12 0.099
II 0.09 0.78 0.32 0.044
III 0.08 1.00 0.46 0.042
APPENDIX II
Spatial Distribution Function
Equation 2a represents the incremental number of inclusions surrounding a
single inclusion in a thin strip of width I::lr:
I::lNS=7TrNS exp (-r2 Ns)l::lr (6)
The exponential term represents the probability that the distance between any
two inclusions lies between rand r + I::lr. The distribution can be normalized by
changing Eq 6 into a continuous distribution, equating the integrand to I, and
solving for the normalization constant, k:
So that
¢(r)=2Nsrexp(-Nsr2) (9)
Equation 9 is the continuous distribution function from which various moments
of r can be calculated. For instance, the average value of r is
(l0)
4 All terms in this section refer to the American Welding Society designations.