ABSTRACT The finite element method (FEM) is used to predict the applied J-integral values in high... more ABSTRACT The finite element method (FEM) is used to predict the applied J-integral values in highly strained tensile panels containing short center cracks. Experimental J-values are obtained by integrating strain and displacement quantities measured along an instrumented contour. FEM plane stress predictions for J-values and crack mouth opening displacements (CMOD) are much larger than experimentally measured values for short cracks (a/WJ and CMOD values. The introduction of a small stiffened zone near the crack tip using an overlay of plane strain elements brings FEM J and CMOD values into close agreement with experimental values. For longer crack lengths, conventional plane stress FEM solutions are adequate to predict J and CMOD values.On utilise la mthode des lments finis en vue de prdire les valeurs de l'intgrale J appliques des panneaux soumis un rgime de tension svre et comportant des fissures contrales courtes. Les valeurs exprimentales de l'Intgrale J sont obtenues en intgrant les dilatations et les dplacements le long d'un contour dment instrument.Il apparat que les prdictions par lments finis des valeurs de J et des dplacements d'ouverture de la portion dbouchante des fissures (CMOD), s'avrent plus leves que les valeurs mesures pour des fissures courtes (a/WOn dmontre que des modifications importantes de la gomtrie n'ont qu'une influence ngligeable sur les valeurs de J et de CMOD, dtermines par lments finis.Le fait d'introduire une zone lgrement raidie au voisinnage de l'extrmit de la fissure, en utilisant notamment un revtement d'lments oprant en tat plan de dformation, a pour consquence de rapprocher ces valeurs de J et de CMOD, des valeurs exprimentales.Dans le cas de longueurs de fissure plus importantes, il s'avre que les solutions conventionnelles par lments finis et tat plan de tension, sont appropries la prdiction des valeurs de J et de CMOD.
Fatigue <html_ent glyph="@amp;" ascii="&"/> Fracture of Engineering Materials and Structures, 2003
ABSTRACT Plasticity induced closure often strongly influences the behaviour of fatigue cracks at ... more ABSTRACT Plasticity induced closure often strongly influences the behaviour of fatigue cracks at engineering scales in metallic materials. Current predictive models generally adopt the effective stress-intensity factor (ΔΚeff = Κmax–Κop) in a Paris law type relationship to quantify crack growth rates. This work describes a 3D finite element study of mode I fatigue crack growth in the small-scale yielding (SSY) regime under a constant amplitude cyclic loading with zero T-stress and a ratio Κmin/Κmax = 0. The material behaviour follows a purely kinematic hardening constitutive model with constant hardening modulus. Dimensional analysis suggests, and the computational results confirm, that the normalized remote opening load value, Κop/Κmax, at each location along the crack front remains unchanged when the peak load (Κmax), thickness (B) and material flow stress (σ0) all vary to maintain a fixed value of . Through parametric computations at various K levels, the results illustrate the effects of normalized peak loads on the through-thickness opening–closing behaviour and the effects of σ0/E, where E denotes material elastic modulus. The examination of deformation fields along the fatigue crack front provides additional insight into the 3D closure process.
ABSTRACT The 3-D small-scale yielding (SSY) model provides a computational framework to study fat... more ABSTRACT The 3-D small-scale yielding (SSY) model provides a computational framework to study fatigue crack growth in thin, metallic components (and test specimens) containing an initially sharp, straight-through crack. This work describes a finite element study of plasticity-induced crack closure in the 3-D SSY model under mode I, constant amplitude cyclic loading with a ratio R=Kmin/Kmax. A purely kinematic hardening model with constant modulus represents the material constitutive behavior. This paper first addresses key computational issues and proposes modeling guidelines leading to 3-D numerical results for fatigue crack growth in SSY that exhibit convergence with mesh refinement. Specifically, computed crack opening loads show an independence of finite element mesh refinement when (a) the plastic zone at peak load encloses more than 10 eight-noded brick elements (b) the reverse plastic zone encloses at least two elements, and (c) the half-thickness has at least five element layers. The paper also describes stress and deformation fields at the crack front for a growing fatigue crack and provides an understanding of localized 3-D effects on the normalized remote opening load value Kop/Kmax. In addition, the computational studies demonstrate that the similarity scaling relationship established for R=0 [Roychowdhury and Dodds, Fatigue Fract. Engng. Mater. Struct. (accepted for publication)] also holds for the non-zero ratio R=0.1––a value commonly adopted in experimental programs. In particular, Kop/Kmax, at each location along the crack front remains unchanged when the peak load (Kmax), thickness (B) and material flow stress (σ0) all vary to maintain a fixed value of .
ABSTRACT Specimen size and loading rate effects on cleavage fracture of ferritic steels tested in... more ABSTRACT Specimen size and loading rate effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain key issues for the application of pre-cracked Charpy specimens. This investigation employs 3-D, nonlinear finite element analyses to assess crack-front stress triaxiality in quasi-static and impact-loaded pre-cracked CVN specimens, with and without side grooves. Crack-front conditions are characterized in terms of the Weibull stress which reflects the statistical effects on cleavage fracture. These 3-D computations indicate that a less strict size/deformation limit, relative to the limits indicated by previous plane-strain analyses, is needed to maintain small-scale yielding conditions at fracture under quasi-static and impact loading conditions. For impact toughness values which violate these size/deformation limits, a toughness scaling methodology is described to remove the effects of constraint loss. The new scaling model also enables prediction of the distribution of quasi-static fracture toughness values from a measured distribution of impact toughness values (and vice versa). This procedure is applied to experimental data obtained from a CrNiMoV pressure vessel steel and accurately predicts quasi-static fracture toughness values in 1T-SE(B) specimens from impact-loaded, pre-cracked CVN specimens. These 3-D analyses also yield η-total values for use in impact testing to infer thickness average and mid-thickness J-values from measured work quantities.
The ASTM Standard Test Method for Plane-Strain Fracture Toughness of metallic Materials (E399-90)... more The ASTM Standard Test Method for Plane-Strain Fracture Toughness of metallic Materials (E399-90) restricts test specimen dimensions to insure the measurement of highly constrained fracture toughness values (K{sub Ic}). These requirements insure small-scale yielding (SSY) conditions at fracture, and thereby the validity of linear elastic fracture mechanics. Recently, Dodds and Anderson have proposed a less restrictive size requirement for cleavage fracture toughness measured in terms of the J-integral (J{sub c}), as given by a, b, B ⥠200 J{sub c}/Ïâ. The size requirement proposed by Dodds and Anderson increases the applicability of fracture toughness experiments by expanding the range of conditions over which fracture toughness data meeting SSY conditions can be reliably measured. This investigation compares the proposed size requirement with that of ASTM Standard Test Method E399 and, by comparison with published experimental data for various alloys, provides validation of the new requirements.
Intergranular failure in metallic materials represents a multiscale damage mechanism: some featur... more Intergranular failure in metallic materials represents a multiscale damage mechanism: some feature of the material microstructure triggers the separation of grain boundaries on the microscale, but the intergranular fractures develop into long cracks on the macroscale. This work develops a multiscale model of grain boundary damage for modeling intergranular delamination—a failure of one particular family of grain boundaries sharing a common normal direction. The key feature of the model is a physically-consistent and mesh independent, multiscale scheme that homogenizes damage at many grain boundaries on the microscale into a single damage parameter on the macroscale to characterize material failure across a plane. The specific application of the damage framework developed here considers delamination failure in modern Al-Li alloys. However, the framework may be readily applied to other metals or composites and to other non-delamination interface geometries—for example, multiple popula...
This work describes a mechanism for the initiation of delamination cracks in Al–Li alloys based o... more This work describes a mechanism for the initiation of delamination cracks in Al–Li alloys based on the soft/stiff character of adjacent grains. Small-scale-yielding, crystal plasticity simulations of divider grain configurations (L-T) reveal an elevated mean stress on grain boundaries. This mean stress increase drives a sharp localization of the Rice-Tracey parameter to the grain boundaries – elevation of the RT parameter indicates favorable conditions for void growth and triggering of delamination cracking, in agreement with the fractography of Ritchie and co-workers. Our simulation results and available experimental evidence indicate delamination initiates typically between soft/stiff grain pairs, often Bs (Bunge-convention Euler angles ϕ1=131°ϕ1=131°, Φ=83°,ϕ2=307°Φ=83°,ϕ2=307°) or S (ϕ1=233°ϕ1=233°, Φ=151°,ϕ2=105°Φ=151°,ϕ2=105°) orientations. The crystal plasticity results and a simple model of a soft/stiff material interface show that mean stress accumulation is a consequence o...
Volume 6: Materials and Fabrication, Parts A and B, 2008
ABSTRACT Transgranular cleavage fracture in the ductile-to-brittle transition region of ferritic ... more ABSTRACT Transgranular cleavage fracture in the ductile-to-brittle transition region of ferritic steels often leads to spectacular and catastrophic failures of engineering structures. Due to the strongly stochastic effects of metallurgical scale inhomogenieties together with the nonlinear mechanical response from plastic deformation, the measured fracture toughness data exhibit a large degree of scatter and a strong dependence on constraint. This has stimulated an increasing amount of research over the past two decades, among which the Weibull stress model originally proposed by the Beremin group has gained much popularity. This model is based on weakest link statistics and provides a framework to quantify the relationship between macro and microscale driving forces for cleavage fracture. It has been successfully applied to predict constraint effects on cleavage fracture and on the scatter of macroscopic fracture toughness values. This paper provides a brief review of the research conducted by the authors in recent years to extend the engineering applicability of the Weibull stress model to predict cleavage fracture in ferritic steels. These recent efforts have introduced a threshold value in the Weibull stress model, introduced more robust calibration methods for determination of model parameters, predicted experimentally observed constraint effects, demonstrated temperature and loading rate effects on the model parameters, and expanded the original Beremin model to include the effects of microcrack nucleation.
ABSTRACT This work explores the effects of grain orientation and T-stress on crack-front shieldin... more ABSTRACT This work explores the effects of grain orientation and T-stress on crack-front shielding and delamination cracking in modern aluminum-lithium alloys. In the crack-arrestor configuration of interest here, a primary crack extends through the grain thickness while triggering delaminations over susceptible grain boundaries that lie normal to the plane of the primary crack. A three-dimensional, small-scale-yielding framework that employs a gradient-enhanced, crystal plasticity material model reveals key features of the strain/stress fields in a simulation of pancake-shaped grains with alternating orientation near a primary crack front. The alternating grain configurations exhibit a soft/stiff behavior and alternating out-of-plane, L-T shear stress-effects observed in recently-published experiments completed by the authors and others on various Al-Li alloys. Both texture effects contribute to highly localized driving forces for delamination cracking while concurrently shielding the primary crack. Moreover, texture does not act to shield the arrestor delamination planes, thereby favoring arrestor delamination development over primary crack growth. A compressive T-stress further enhances shielding of the primary crack-a result which aids in understanding marked differences in observed fracture behavior of tested M(T) and C(T) specimens of Al-Li alloys.
ABSTRACT This paper investigates the effects of in-plane constraint on 3-D fatigue crack closure ... more ABSTRACT This paper investigates the effects of in-plane constraint on 3-D fatigue crack closure in the small-scale yielding regime. The finite element analyses grow a sharp, straight-through crack in a modified boundary layer model under mode I, constant amplitude cyclic loading with prescribed but independent peak values of stress intensity factor, Kmax, and the T-stress, Tmax. A purely kinematic hardening law with constant modulus represents the material constitutive behavior. The computational results demonstrate that a two parameter characterization of crack tip fields in terms of and Tmax/σ0, where σ0 denotes the yield stress of the material, correlates successfully the normalized opening load Kop/Kmax across variations of thickness (B), constraint level and material flow properties. Both negative and positive T-stress reduce the through-thickness variation in local opening load levels along the crack front. A negative T-stress increases Kop/Kmax values, particularly at low peak loads where the plastic zone size remains a fraction of the thickness; a positive T-stress has limited effect on Kop/Kmax values. The fringe plots of individual plastic strain components reveal (a) in the absence of T-stress (Tmax/σ0=0), plastic contraction in the thickness direction compensates primarily for permanent stretching in the direction normal to the crack plane required for closure, (b) for negative T-stress (Tmax/σ0&lt;0), plastic contraction in the in-plane transverse direction contributes the larger share of material flowing into the normal direction, and (c) for positive T-stress (Tmax/σ0&gt;0), both in-plane directions experience permanent stretching and the thickness direction alone undergoes plastic contraction.
ABSTRACT The implementation of generalized FEM software has progressed to a stage where maintaina... more ABSTRACT The implementation of generalized FEM software has progressed to a stage where maintainability, expandability, and reliability are features of major importance. Software virtual computing systems are a way to significantly reduce the effort related to developing FEM codes while at the same time providing a mechanism to achieve these and other desirable features. FINITE is an example of what can be done with a small staff and a good system nucleus.
ABSTRACT This study examines crack front length and constraint loss effects on cleavage fracture ... more ABSTRACT This study examines crack front length and constraint loss effects on cleavage fracture toughness in ferritic steels at temperatures in the ductile-to-brittle transition region. A local approach for fracture at the micro-scale of the material based on the Weibull stress is coupled with very detailed three-dimensional models of deep-notch bend specimens. A new non-dimensional function g(M) derived from the Weibull stress density describes the overall constraint level in a specimen. This function remains identical for all geometrically similar specimens regardless of their absolute sizes, and thus provides a computationally simple approach to construct (three-dimensional) fracture driving force curves w vs. J, for each absolute size of interest. Proposed modifications of the conventional, two-parameter Weibull stress expression for cumulative failure probability introduce a new threshold parameter w–min. This parameter has a simple calibration procedure requiring no additional experimental data. The use of a toughness scaling model including w–min&gt;0 increases the deformation level at which the CVN size specimen loses constraint compared to a 1TSE(B) specimen, which improves the agreement of computational predictions and experimental estimations. Finally the effects of specimen size and constraint loss on the cleavage fracture reference temperature T 0 as determined using the new standard ASTM E1921 are investigated using Monte Carlo simulation together with the new toughness scaling model.
The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two mic... more The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters $$(m,\sigma _u ) $$ . Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide
ABSTRACT The effects of modeling parameters on the response of finite element representations of ... more ABSTRACT The effects of modeling parameters on the response of finite element representations of reinforced concrete members are examined. The convergence of load deflection curves and cracking patterns is studied. Nonlinear behavior is limited to cracking of the concrete and yielding of the reinforcement. The smeared crack representation is governed by a limiting tensile stress criterion. Concrete is treated as linear elastic in compression. Reinforcement has a bilinear stress-strain curve. Constant strain bar elements and rectangular isoparametric elements model the steel and concrete, respectively. Analyses are performed for flexural members under both a uniformly distributed load and a concentrated load at midspan, using a minimum of three variations in grid refinement.
International Journal of Solids and Structures, 2009
This paper describes studies of the near tip fields and the effects on void growth rates for a st... more This paper describes studies of the near tip fields and the effects on void growth rates for a steadily advancing crack through a ductile metal in the presence of hydrogen, under plane-strain and quasi-static conditions. The computational model determines directly the deformation history of a steadily propagating crack without the need for a priori (transient) analysis that considers blunting of
ABSTRACT The finite element method (FEM) is used to predict the applied J-integral values in high... more ABSTRACT The finite element method (FEM) is used to predict the applied J-integral values in highly strained tensile panels containing short center cracks. Experimental J-values are obtained by integrating strain and displacement quantities measured along an instrumented contour. FEM plane stress predictions for J-values and crack mouth opening displacements (CMOD) are much larger than experimentally measured values for short cracks (a/WJ and CMOD values. The introduction of a small stiffened zone near the crack tip using an overlay of plane strain elements brings FEM J and CMOD values into close agreement with experimental values. For longer crack lengths, conventional plane stress FEM solutions are adequate to predict J and CMOD values.On utilise la mthode des lments finis en vue de prdire les valeurs de l&#39;intgrale J appliques des panneaux soumis un rgime de tension svre et comportant des fissures contrales courtes. Les valeurs exprimentales de l&#39;Intgrale J sont obtenues en intgrant les dilatations et les dplacements le long d&#39;un contour dment instrument.Il apparat que les prdictions par lments finis des valeurs de J et des dplacements d&#39;ouverture de la portion dbouchante des fissures (CMOD), s&#39;avrent plus leves que les valeurs mesures pour des fissures courtes (a/WOn dmontre que des modifications importantes de la gomtrie n&#39;ont qu&#39;une influence ngligeable sur les valeurs de J et de CMOD, dtermines par lments finis.Le fait d&#39;introduire une zone lgrement raidie au voisinnage de l&#39;extrmit de la fissure, en utilisant notamment un revtement d&#39;lments oprant en tat plan de dformation, a pour consquence de rapprocher ces valeurs de J et de CMOD, des valeurs exprimentales.Dans le cas de longueurs de fissure plus importantes, il s&#39;avre que les solutions conventionnelles par lments finis et tat plan de tension, sont appropries la prdiction des valeurs de J et de CMOD.
Fatigue <html_ent glyph="@amp;" ascii="&"/> Fracture of Engineering Materials and Structures, 2003
ABSTRACT Plasticity induced closure often strongly influences the behaviour of fatigue cracks at ... more ABSTRACT Plasticity induced closure often strongly influences the behaviour of fatigue cracks at engineering scales in metallic materials. Current predictive models generally adopt the effective stress-intensity factor (ΔΚeff = Κmax–Κop) in a Paris law type relationship to quantify crack growth rates. This work describes a 3D finite element study of mode I fatigue crack growth in the small-scale yielding (SSY) regime under a constant amplitude cyclic loading with zero T-stress and a ratio Κmin/Κmax = 0. The material behaviour follows a purely kinematic hardening constitutive model with constant hardening modulus. Dimensional analysis suggests, and the computational results confirm, that the normalized remote opening load value, Κop/Κmax, at each location along the crack front remains unchanged when the peak load (Κmax), thickness (B) and material flow stress (σ0) all vary to maintain a fixed value of . Through parametric computations at various K levels, the results illustrate the effects of normalized peak loads on the through-thickness opening–closing behaviour and the effects of σ0/E, where E denotes material elastic modulus. The examination of deformation fields along the fatigue crack front provides additional insight into the 3D closure process.
ABSTRACT The 3-D small-scale yielding (SSY) model provides a computational framework to study fat... more ABSTRACT The 3-D small-scale yielding (SSY) model provides a computational framework to study fatigue crack growth in thin, metallic components (and test specimens) containing an initially sharp, straight-through crack. This work describes a finite element study of plasticity-induced crack closure in the 3-D SSY model under mode I, constant amplitude cyclic loading with a ratio R=Kmin/Kmax. A purely kinematic hardening model with constant modulus represents the material constitutive behavior. This paper first addresses key computational issues and proposes modeling guidelines leading to 3-D numerical results for fatigue crack growth in SSY that exhibit convergence with mesh refinement. Specifically, computed crack opening loads show an independence of finite element mesh refinement when (a) the plastic zone at peak load encloses more than 10 eight-noded brick elements (b) the reverse plastic zone encloses at least two elements, and (c) the half-thickness has at least five element layers. The paper also describes stress and deformation fields at the crack front for a growing fatigue crack and provides an understanding of localized 3-D effects on the normalized remote opening load value Kop/Kmax. In addition, the computational studies demonstrate that the similarity scaling relationship established for R=0 [Roychowdhury and Dodds, Fatigue Fract. Engng. Mater. Struct. (accepted for publication)] also holds for the non-zero ratio R=0.1––a value commonly adopted in experimental programs. In particular, Kop/Kmax, at each location along the crack front remains unchanged when the peak load (Kmax), thickness (B) and material flow stress (σ0) all vary to maintain a fixed value of .
ABSTRACT Specimen size and loading rate effects on cleavage fracture of ferritic steels tested in... more ABSTRACT Specimen size and loading rate effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain key issues for the application of pre-cracked Charpy specimens. This investigation employs 3-D, nonlinear finite element analyses to assess crack-front stress triaxiality in quasi-static and impact-loaded pre-cracked CVN specimens, with and without side grooves. Crack-front conditions are characterized in terms of the Weibull stress which reflects the statistical effects on cleavage fracture. These 3-D computations indicate that a less strict size/deformation limit, relative to the limits indicated by previous plane-strain analyses, is needed to maintain small-scale yielding conditions at fracture under quasi-static and impact loading conditions. For impact toughness values which violate these size/deformation limits, a toughness scaling methodology is described to remove the effects of constraint loss. The new scaling model also enables prediction of the distribution of quasi-static fracture toughness values from a measured distribution of impact toughness values (and vice versa). This procedure is applied to experimental data obtained from a CrNiMoV pressure vessel steel and accurately predicts quasi-static fracture toughness values in 1T-SE(B) specimens from impact-loaded, pre-cracked CVN specimens. These 3-D analyses also yield η-total values for use in impact testing to infer thickness average and mid-thickness J-values from measured work quantities.
The ASTM Standard Test Method for Plane-Strain Fracture Toughness of metallic Materials (E399-90)... more The ASTM Standard Test Method for Plane-Strain Fracture Toughness of metallic Materials (E399-90) restricts test specimen dimensions to insure the measurement of highly constrained fracture toughness values (K{sub Ic}). These requirements insure small-scale yielding (SSY) conditions at fracture, and thereby the validity of linear elastic fracture mechanics. Recently, Dodds and Anderson have proposed a less restrictive size requirement for cleavage fracture toughness measured in terms of the J-integral (J{sub c}), as given by a, b, B ⥠200 J{sub c}/Ïâ. The size requirement proposed by Dodds and Anderson increases the applicability of fracture toughness experiments by expanding the range of conditions over which fracture toughness data meeting SSY conditions can be reliably measured. This investigation compares the proposed size requirement with that of ASTM Standard Test Method E399 and, by comparison with published experimental data for various alloys, provides validation of the new requirements.
Intergranular failure in metallic materials represents a multiscale damage mechanism: some featur... more Intergranular failure in metallic materials represents a multiscale damage mechanism: some feature of the material microstructure triggers the separation of grain boundaries on the microscale, but the intergranular fractures develop into long cracks on the macroscale. This work develops a multiscale model of grain boundary damage for modeling intergranular delamination—a failure of one particular family of grain boundaries sharing a common normal direction. The key feature of the model is a physically-consistent and mesh independent, multiscale scheme that homogenizes damage at many grain boundaries on the microscale into a single damage parameter on the macroscale to characterize material failure across a plane. The specific application of the damage framework developed here considers delamination failure in modern Al-Li alloys. However, the framework may be readily applied to other metals or composites and to other non-delamination interface geometries—for example, multiple popula...
This work describes a mechanism for the initiation of delamination cracks in Al–Li alloys based o... more This work describes a mechanism for the initiation of delamination cracks in Al–Li alloys based on the soft/stiff character of adjacent grains. Small-scale-yielding, crystal plasticity simulations of divider grain configurations (L-T) reveal an elevated mean stress on grain boundaries. This mean stress increase drives a sharp localization of the Rice-Tracey parameter to the grain boundaries – elevation of the RT parameter indicates favorable conditions for void growth and triggering of delamination cracking, in agreement with the fractography of Ritchie and co-workers. Our simulation results and available experimental evidence indicate delamination initiates typically between soft/stiff grain pairs, often Bs (Bunge-convention Euler angles ϕ1=131°ϕ1=131°, Φ=83°,ϕ2=307°Φ=83°,ϕ2=307°) or S (ϕ1=233°ϕ1=233°, Φ=151°,ϕ2=105°Φ=151°,ϕ2=105°) orientations. The crystal plasticity results and a simple model of a soft/stiff material interface show that mean stress accumulation is a consequence o...
Volume 6: Materials and Fabrication, Parts A and B, 2008
ABSTRACT Transgranular cleavage fracture in the ductile-to-brittle transition region of ferritic ... more ABSTRACT Transgranular cleavage fracture in the ductile-to-brittle transition region of ferritic steels often leads to spectacular and catastrophic failures of engineering structures. Due to the strongly stochastic effects of metallurgical scale inhomogenieties together with the nonlinear mechanical response from plastic deformation, the measured fracture toughness data exhibit a large degree of scatter and a strong dependence on constraint. This has stimulated an increasing amount of research over the past two decades, among which the Weibull stress model originally proposed by the Beremin group has gained much popularity. This model is based on weakest link statistics and provides a framework to quantify the relationship between macro and microscale driving forces for cleavage fracture. It has been successfully applied to predict constraint effects on cleavage fracture and on the scatter of macroscopic fracture toughness values. This paper provides a brief review of the research conducted by the authors in recent years to extend the engineering applicability of the Weibull stress model to predict cleavage fracture in ferritic steels. These recent efforts have introduced a threshold value in the Weibull stress model, introduced more robust calibration methods for determination of model parameters, predicted experimentally observed constraint effects, demonstrated temperature and loading rate effects on the model parameters, and expanded the original Beremin model to include the effects of microcrack nucleation.
ABSTRACT This work explores the effects of grain orientation and T-stress on crack-front shieldin... more ABSTRACT This work explores the effects of grain orientation and T-stress on crack-front shielding and delamination cracking in modern aluminum-lithium alloys. In the crack-arrestor configuration of interest here, a primary crack extends through the grain thickness while triggering delaminations over susceptible grain boundaries that lie normal to the plane of the primary crack. A three-dimensional, small-scale-yielding framework that employs a gradient-enhanced, crystal plasticity material model reveals key features of the strain/stress fields in a simulation of pancake-shaped grains with alternating orientation near a primary crack front. The alternating grain configurations exhibit a soft/stiff behavior and alternating out-of-plane, L-T shear stress-effects observed in recently-published experiments completed by the authors and others on various Al-Li alloys. Both texture effects contribute to highly localized driving forces for delamination cracking while concurrently shielding the primary crack. Moreover, texture does not act to shield the arrestor delamination planes, thereby favoring arrestor delamination development over primary crack growth. A compressive T-stress further enhances shielding of the primary crack-a result which aids in understanding marked differences in observed fracture behavior of tested M(T) and C(T) specimens of Al-Li alloys.
ABSTRACT This paper investigates the effects of in-plane constraint on 3-D fatigue crack closure ... more ABSTRACT This paper investigates the effects of in-plane constraint on 3-D fatigue crack closure in the small-scale yielding regime. The finite element analyses grow a sharp, straight-through crack in a modified boundary layer model under mode I, constant amplitude cyclic loading with prescribed but independent peak values of stress intensity factor, Kmax, and the T-stress, Tmax. A purely kinematic hardening law with constant modulus represents the material constitutive behavior. The computational results demonstrate that a two parameter characterization of crack tip fields in terms of and Tmax/σ0, where σ0 denotes the yield stress of the material, correlates successfully the normalized opening load Kop/Kmax across variations of thickness (B), constraint level and material flow properties. Both negative and positive T-stress reduce the through-thickness variation in local opening load levels along the crack front. A negative T-stress increases Kop/Kmax values, particularly at low peak loads where the plastic zone size remains a fraction of the thickness; a positive T-stress has limited effect on Kop/Kmax values. The fringe plots of individual plastic strain components reveal (a) in the absence of T-stress (Tmax/σ0=0), plastic contraction in the thickness direction compensates primarily for permanent stretching in the direction normal to the crack plane required for closure, (b) for negative T-stress (Tmax/σ0&lt;0), plastic contraction in the in-plane transverse direction contributes the larger share of material flowing into the normal direction, and (c) for positive T-stress (Tmax/σ0&gt;0), both in-plane directions experience permanent stretching and the thickness direction alone undergoes plastic contraction.
ABSTRACT The implementation of generalized FEM software has progressed to a stage where maintaina... more ABSTRACT The implementation of generalized FEM software has progressed to a stage where maintainability, expandability, and reliability are features of major importance. Software virtual computing systems are a way to significantly reduce the effort related to developing FEM codes while at the same time providing a mechanism to achieve these and other desirable features. FINITE is an example of what can be done with a small staff and a good system nucleus.
ABSTRACT This study examines crack front length and constraint loss effects on cleavage fracture ... more ABSTRACT This study examines crack front length and constraint loss effects on cleavage fracture toughness in ferritic steels at temperatures in the ductile-to-brittle transition region. A local approach for fracture at the micro-scale of the material based on the Weibull stress is coupled with very detailed three-dimensional models of deep-notch bend specimens. A new non-dimensional function g(M) derived from the Weibull stress density describes the overall constraint level in a specimen. This function remains identical for all geometrically similar specimens regardless of their absolute sizes, and thus provides a computationally simple approach to construct (three-dimensional) fracture driving force curves w vs. J, for each absolute size of interest. Proposed modifications of the conventional, two-parameter Weibull stress expression for cumulative failure probability introduce a new threshold parameter w–min. This parameter has a simple calibration procedure requiring no additional experimental data. The use of a toughness scaling model including w–min&gt;0 increases the deformation level at which the CVN size specimen loses constraint compared to a 1TSE(B) specimen, which improves the agreement of computational predictions and experimental estimations. Finally the effects of specimen size and constraint loss on the cleavage fracture reference temperature T 0 as determined using the new standard ASTM E1921 are investigated using Monte Carlo simulation together with the new toughness scaling model.
The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two mic... more The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters $$(m,\sigma _u ) $$ . Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide
ABSTRACT The effects of modeling parameters on the response of finite element representations of ... more ABSTRACT The effects of modeling parameters on the response of finite element representations of reinforced concrete members are examined. The convergence of load deflection curves and cracking patterns is studied. Nonlinear behavior is limited to cracking of the concrete and yielding of the reinforcement. The smeared crack representation is governed by a limiting tensile stress criterion. Concrete is treated as linear elastic in compression. Reinforcement has a bilinear stress-strain curve. Constant strain bar elements and rectangular isoparametric elements model the steel and concrete, respectively. Analyses are performed for flexural members under both a uniformly distributed load and a concentrated load at midspan, using a minimum of three variations in grid refinement.
International Journal of Solids and Structures, 2009
This paper describes studies of the near tip fields and the effects on void growth rates for a st... more This paper describes studies of the near tip fields and the effects on void growth rates for a steadily advancing crack through a ductile metal in the presence of hydrogen, under plane-strain and quasi-static conditions. The computational model determines directly the deformation history of a steadily propagating crack without the need for a priori (transient) analysis that considers blunting of
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Papers by Robert Dodds