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J. H. Chang - One of the best experts on this subject based on the ideXlab platform.
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Evaluation of Mixed-Mode Stress Intensity Factors for a Sharp Notch-Tip With Curved and Stressed Edges
Journal of Applied Mechanics, 2009Co-Authors: J. H. Chang, J. F. FanAbstract:For a sharp Notch with curved edges and subjected to surface tractions along the edges, the fracture parameters (in particular, the stress intensity factors and the size of a singular-dominant zone) are significantly affected by the near-Tip geometric and loading conditions. In this paper, a pair of contour integrals termed J kR is presented for calculating the mixed-mode stress intensity factors at such a sharp Notch-Tip. Furthermore, by proper use of the integrals, the extent of the singular-dominant zone can be effectively characterized. Since no a priori auxiliary (or, complementary) solutions are required in its formulation, the approach appears to be feasible for problems of arbitrary Notch angles and curved shapes. Also, no special treatments are required for the modeling of the near-Tip singular behavior so that the integration can be performed by direct use of numerical schemes such as finite element method.
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Calculation of mixed-mode stress field at a sharp Notch Tip using M1ɛ-integral
Computational Mechanics, 2003Co-Authors: J. H. Chang, W. H. WuAbstract:Direct computation of the mixed-mode stress field at a sharp Notch Tip appears to be difficult in that the mode I and mode II asymptotic stresses are in general governed by different orders of singularity. In this paper, we first present a path-independent integral termed M1ɛ. The relation between M1ɛ and the generalized stress intensity factors is then derived and expressed as function of the Notch angle. Once the M1ɛ-integrals are accurately computed, the generalized SIF's and, consequently, the asymptotic mixed-mode stress field can thus be properly determined. No extra complementary solutions are required in the formulation. Further, no particular singular elements are required when the integration is performed by using finite elements.
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Calculation of mixed-mode stress field at a sharp Notch Tip using M _1ɛ-integral
Computational Mechanics, 2003Co-Authors: J. H. Chang, W. H. WuAbstract:Direct computation of the mixed-mode stress field at a sharp Notch Tip appears to be difficult in that the mode I and mode II asymptotic stresses are in general governed by different orders of singularity. In this paper, we first present a path-independent integral termed M _1ɛ. The relation between M _1ɛ and the generalized stress intensity factors is then derived and expressed as function of the Notch angle. Once the M _1ɛ-integrals are accurately computed, the generalized SIF's and, consequently, the asymptotic mixed-mode stress field can thus be properly determined. No extra complementary solutions are required in the formulation. Further, no particular singular elements are required when the integration is performed by using finite elements.
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Finite element calculation of elastodynamic stress field around a Notch Tip via contour integrals
International Journal of Solids and Structures, 2003Co-Authors: J. H. ChangAbstract:Abstract Direct computation of the mixed-mode dynamic asymptotic stress field around a Notch Tip is difficult because the mode I and mode II stresses are in general governed by different orders of singularity. In this paper, we propose a pair of elastodynamic contour integrals J kR ( t ). The integrals are shown to be path-independent in a modified sense and so they can be accurately evaluated with finite element solutions. Also, by defining a pair of generalized stress intensity factors (SIFs) K I, β ( t ) and K II, β ( t ), the relationship between J kR ( t ) and the SIF’s is derived and expressed as functions of the Notch angle β . Once the J kR ( t )-integrals are accurately computed, the generalized SIF’s and, consequently, the asymptotic mixed-mode stress field can then be properly determined. No particular singular elements are required in the calculation. The proposed numerical scheme can be used to investigate the dynamic amplifying effect in the near-Tip stress field.
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Evaluation of the stress field around a Notch Tip using contour integrals
International Journal of Engineering Science, 2002Co-Authors: J. H. Chang, L.k. KangAbstract:Abstract The mode I and mode II asymptotic stresses around a Notch Tip are in general governed by different orders of singularity. Direct computation of the mixed-mode near-Tip stress field therefore appears to be difficult. In this paper, we propose a pair of contour integrals J kR . The integrals are shown to be path-independent in a modified sense and so they can be accurately evaluated with finite element solutions. As an aside, by defining a pair of generalized stress intensity factors (SIFs) ( K I ) β and ( K II ) β , the relationship between J kR and the SIFs is derived and expressed as functions of the Notch angle β . Once the J kR -integrals are accurately computed, the generalized SIFs and, consequently, the asymptotic mixed-mode stress field can then be properly determined. The feasibility of our formulation is demonstrated in two numerical examples, where various instances with different Notch angles are considered. No particular singular elements are used in this study.
Y C Gao - One of the best experts on this subject based on the ideXlab platform.
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Analytical solution to a Notch Tip field in rubber-like materials under tension
International Journal of Solids and Structures, 1999Co-Authors: Y C Gao, Tianjie GaoAbstract:The large strain field near a Notch Tip in some kinds of rubber materials under tension is reinvestigated. The completely analytical solution of the mapping functions are obtained for both expanding sector and shrinking sector. The stress singularity is expressed by Notch angle precisely. This solution is derived from a typical elastic law but it is proved to be valid for a wide kind of rubber material.
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Large strain field near a Notch-Tip under tension
Theoretical and Applied Fracture Mechanics, 1997Co-Authors: Z.q. Wang, Y C GaoAbstract:Abstract This paper considers the plane strain Notch-Tip filed in a rubber-like material under tension. Based on a new constitutive relation, the asymptotic equations of the near Tip field are derived and solved. It is shown that the Notch Tip field is composed of two narrowing sectors and an expanding sector. The dominant stress and strain near the Notch Tip are found to be in a state of uniaxial tension.
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Notch-Tip fields in rubber-like materials under tension and shear mixed load
International Journal of Fracture, 1996Co-Authors: Y C Gao, T. S. GaoAbstract:This paper introduces a new method to solve the singular stress strain field near a Notch-Tip in rubber-like materials. The constitutive relation used herein is valid even when the strain tends to infinity. The singular field is divided into shrinking sectors and expanding sectors for which the asymptotic equations are derived separately. The solution to the expanding sector is obtained analytically while that for the shrinking sectors are solved numerically. The singular behavior of the Notch Tip field is revealed clearly.
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Stress singularity near the Notch Tip of a rubber-like specimen under tension
European Journal of Mechanics A-solids, 1996Co-Authors: Y C Gao, B. LiuAbstract:Using Gao's elastic constitutive relation [Gao, 1990] the present paper analyses the stress strain singularity near the Notch Tip of a rubber-like specimen under the condition of plane strain tension. The asymptotic equation of the Notch-Tip field for the large deformation case is solved numerically, and the relation between the stress singularity and the Notch angle is obtained. Finally, the results are compared with those for small strain deformation.
Michael T. Hendry - One of the best experts on this subject based on the ideXlab platform.
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fracture behaviour at the sharp Notch Tip of high strength rail steels influence of stress triaxiality
Engineering Fracture Mechanics, 2017Co-Authors: P.-y. Ben Jar, Michael T. HendryAbstract:Abstract This work explores the possibility of using mechanical properties of two types of Notch-free specimens to evaluate crack growth resistance of a sharp Notch Tip. Equivalent plastic fracture strain ( e eq f , η av ) of pre-cracked single-edged-Notched bending (SENB) specimen is estimated using a model that correlates e eq f , η av for Notch-free specimens with their average stress triaxiality. Finite element modelling is used to establish constitutive equations and variations of stress triaxiality in the two types of Notch-free specimens and the pre-cracked SENB specimen. All of the information is then used to predict the critical strain energy density factor ( S c ) at a characteristic distance ahead of the sharp Notch Tip and the corresponding stress intensity factor (KSc) for three high strength rail steels. The predicted KSc values are compared with the experimentally measured mode I critical stress intensity factor (KIc) at temperatures 23, −10, and −40 °C. The results show good agreement between KSc and KIc in their variation with temperature, possibly because S c takes into account both distortional and dilatational strain energy density of the sharp Notch Tip under small-scale yielding. Results from the study also suggest that a correlation should exist among mechanical properties for Notch-free and Notched specimens, though their apparent trend of change with temperature may not bear any similarity.
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Fracture behaviour at the sharp Notch Tip of high strength rail steels – Influence of stress triaxiality
Engineering Fracture Mechanics, 2017Co-Authors: P.-y. Ben Jar, Michael T. HendryAbstract:Abstract This work explores the possibility of using mechanical properties of two types of Notch-free specimens to evaluate crack growth resistance of a sharp Notch Tip. Equivalent plastic fracture strain ( e eq f , η av ) of pre-cracked single-edged-Notched bending (SENB) specimen is estimated using a model that correlates e eq f , η av for Notch-free specimens with their average stress triaxiality. Finite element modelling is used to establish constitutive equations and variations of stress triaxiality in the two types of Notch-free specimens and the pre-cracked SENB specimen. All of the information is then used to predict the critical strain energy density factor ( S c ) at a characteristic distance ahead of the sharp Notch Tip and the corresponding stress intensity factor (KSc) for three high strength rail steels. The predicted KSc values are compared with the experimentally measured mode I critical stress intensity factor (KIc) at temperatures 23, −10, and −40 °C. The results show good agreement between KSc and KIc in their variation with temperature, possibly because S c takes into account both distortional and dilatational strain energy density of the sharp Notch Tip under small-scale yielding. Results from the study also suggest that a correlation should exist among mechanical properties for Notch-free and Notched specimens, though their apparent trend of change with temperature may not bear any similarity.
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Critical Strain and Damage Evolution for Crack Growth From a Sharp Notch Tip of High-Strength Steel
Volume 6A: Materials and Fabrication, 2016Co-Authors: Ben Jar, Michael T. HendryAbstract:This paper proposes details of an approach that uses expressions of fracture strain and damage evolution as functions of stress triaxiality for Notch-free specimens to predict their values for crack growth from a sharp Notch Tip of a single-edge-Notched bend (SENB) specimen. Experimental testing and finite element (FE) modelling are used to determine the basic mechanical properties and deformation behaviour of those specimens, which are needed to calibrate model constants in the proposed approach and to validate prediction from the approach. Three types of mechanical testing were conducted, using standard smooth tensile, short-gauged tensile and standard SENB specimens. The FE modeling is to establish constitutive relationship between stress and strain for Notch-free specimens so that the FE modeling can be used to determine parameters such as stress triaxiality and unloading modulus for the prediction of fracture strain and damage evolution at the sharp Notch Tip of SENB specimen. The study will then examine whether the proposed approach can predict the trend of variation for fracture toughness among three high-strength steels, which is an on-going study and the results will be presented in the conference.
Raja K. Mishra - One of the best experts on this subject based on the ideXlab platform.
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Finite element simulations of Notch Tip fields in magnesium single crystals
International Journal of Fracture, 2014Co-Authors: V. Kaushik, R. Narasimhan, Raja K. MishraAbstract:Recent experiments using three point bend specimens of Mg single crystals have revealed that tensile twins of $$\{10\bar{1}2\}$$ { 10 1 ¯ 2 } -type form profusely near a Notch Tip and enhance the fracture toughness through large plastic dissipation. In this work, 3D finite element simulations of these experiments are carried out using a crystal plasticity framework which includes slip and twinning to gain insights on the mechanics of fracture. The predicted load–displacement curves, slip and tensile twinning activities from finite element analysis corroborate well with the experimental observations. The numerical results are used to explore the 3D nature of the crack Tip stress, plastic slip and twin volume fraction distributions near the Notch root. The occurrence of tensile twinning is rationalized from the variation of normal stress ahead of the Notch Tip. Further, deflection of the crack path at twin–twin intersections observed in the experiments is examined from an energy standpoint by modeling discrete twins close to the Notch root.
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Finite element simulations of Notch Tip fields in magnesium single crystals
International Journal of Fracture, 2014Co-Authors: Kaushik, R. Narasimhan, Raja K. MishraAbstract:Recent experiments using three point bend specimens of Mg single crystals have revealed that tensile twins of {10 (1) over bar2}-type form profusely near a Notch Tip and enhance the fracture toughness through large plastic dissipation. In this work, 3D finite element simulations of these experiments are carried out using a crystal plasticity framework which includes slip and twinning to gain insights on the mechanics of fracture. The predicted load-displacement curves, slip and tensile twinning activities from finite element analysis corroborate well with the experimental observations. The numerical results are used to explore the 3D nature of the crack Tip stress, plastic slip and twin volume fraction distributions near the Notch root. The occurrence of tensile twinning is rationalized from the variation of normal stress ahead of the Notch Tip. Further, deflection of the crack path at twin-twin intersections observed in the experiments is examined from an energy standpoint by modeling discrete twins close to the Notch root.
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Numerical simulations of void growth near a Notch Tip in ductile single crystals
Mechanics of Materials, 2009Co-Authors: Amol G. Thakare, R. Narasimhan, Raja K. MishraAbstract:The objective of this work is to study the growth of a cylindrical void ahead of a Notch Tip in ductile FCC single crystals under mode I, plane strain, small scale yielding (SSY) conditions. To this end, finite element simulations are performed within crystal plasticity framework neglecting elastic anisotropy. Attention is focussed on the effects of crystal hardening, ratio of void diameter to spacing from the Notch and crystal orientation on plastic flow localization in the ligament connecting the Notch and the void as well as their growth. The results show strong interaction between shear bands emanating from the Notch and angular sectors of single slip forming around the void leading to intense plastic strain development in the ligament. Further, the ductile fracture processes are retarded by increase in hardening of the single crystal and decrease in ratio of void diameter to spacing from the Notch. Also, a strong influence of crystal orientation on near-Tip void growth and plastic slip band development is observed. Finally, the synergistic, cooperative growth of mulTiple voids ahead of the Notch Tip is examined.
Thomas W Shield - One of the best experts on this subject based on the ideXlab platform.
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Experimental study of the deformation near a Notch Tip in copper and copper-beryllium single crystals
Journal of the Mechanics and Physics of Solids, 2001Co-Authors: Wendy C. Crone, Thomas W ShieldAbstract:Abstract The plastic deformation around a Notch Tip within ductile single crystal material was investigated experimentally. Moire microscopy was used to measure the strain field on the surface of bending samples of Orientation II with a Notch on the (0 1 0) plane and its Tip along the [ 1 0 1] direction. The results of tests conducted on copper and copper–beryllium single crystals are compared to analytical solutions, numerical calculations, and prior experiments on samples of Orientation I with a Notch on the (1 0 1) plane and its Tip along the [1 0 1 ] direction. Distinct sectors with sharp sector boundaries are observed in experiments as were predicted analytically by Rice (Mech. Mater. 6 (1987) 301). However, Rice predicted that both Orientations I and II would give rise to the same sectors. It is found that experimental results for these two orientations differ and neither set of results agree with the analytical solution. In both orientations, the sector boundaries do not exclusively correspond to angles at which slip and kink can occur in these crystallographic orientations. The experiments also lead to the conclusion that some sectors in the deformation field remain elastic even after large amounts of deformation have occurred elsewhere. Based on the optical observations and strain measurements, a stress field is presented for Orientation II.
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an experimental study of the plastic strain fields near a Notch Tip in a copper single crystal during loading
Acta Materialia, 1996Co-Authors: Thomas W ShieldAbstract:Abstract The strain fields near a 100 μm Notch in a single crystal of copper have been measured. The Notch lies in a {{110}} plane and prospective crack growth is in a 〈100〉 direction. The surface strains were measured during loading using a microscopic moire method. Data from six load levels are presented for an approx. 2 by 2.5 mm region on one side of the Notch Tip. These data show that the patchy strain field observed in an iron-silicon single crystal with an identical orientation also occurred in this copper single crystal. Four (8 symmetric) strain sectors form, however, the strain field does not develop in a proportional manner. Initially slip occurs in the second sector and this is visible as discrete slip bands. This deformation leads to the formation of a fan type strain field in the third sector as the overall strain level increases.
