Ductile fracture by multiple void growth and interaction ahead of a notch tip in polycrystalline plastic solids

The objectives of this paper are to study the effects of plastic anisotropy and evolution in crystallographic texture with deformation on the ductile fracture behaviour of polycrystalline solids. To this end, numerical simulations of multiple void growth and interaction ahead of a notch tip are performed under mode I, plane strain, small scale yielding conditions using two approaches. The first approach is based on the Hill yield theory, while the second employs crystal plasticity constitutive equations and a Taylor-type homogenization in order to represent the ductile polycrystalline solid. The initial textures pertaining to continuous cast Al–Mg AA5754 sheets in recrystallized and cold rolled conditions are considered. The former is nearly-isotropic, while the latter displays pronounced anisotropy. The results indicate distinct changes in texture in the ligaments bridging the voids ahead of the notch tip with increase in load level which gives rise to retardation in porosity evolution and increase in tearing resistance for both materials.     

Effects of plastic anisotropy on crack-tip behaviour

For a crack in a homogeneous material the effect of plastic anisotropy on crack-tip blunting and on the near-tip stress and strain fields is analyzed numerically. The full finite strain analyses are carried out for plane strain under small scale yielding conditions, with purely symmetric mode I loading remote from the crack-tip. In cases where the principal axes of the anisotropy are inclined to the plane of the crack it is found that the plastic zones as well as the stress and strain fields just around the blunted tip of the crack become non-symmetric. In these cases the peak strain on the blunted tip occurs off the center line of the crack, thus indicating that the crack may want to grow in a different direction. When the anisotropic axes are parallel to the crack symmetry is retained, but the plastic zones and the near-tip fields still differ from those predicted by standard isotropic plasticity.     

Plane strain crack closure and cyclic hardening

This study is focused on the understanding of the mechanical effects of cyclic hardening on crack tip plasticity and on plasticity-induced crack closure. Various finite element analyses were conducted using abaqus. Cyclic hardening is found to affect both crack closure and the shape of the plastic zone at the crack tip. Crack growth modelling in plane strain conditions in a cyclically hardening material is discussed. An empirical formula is provided which allows the calculation of the crack tip plastic zone size under plane strain conditions in a cyclically hardening material. The effects of overloads are also examined.     

无取向硅钢形变储能取向依赖性及其对再结晶织构的影响

采用晶体塑性有限元模拟与实验相结合的方式,研究无取向硅钢冷轧过程中不同初始织构组分的取向流动与形变储能累积。结果表明:冷轧后形成了较强的α,γ形变织构和较弱的λ形变织构。再结晶织构由γ,α,η和λ织构组成,其取向密度依赖于冷轧压下率。随冷轧压下率增大,λ再结晶织构逐渐增强,η织构先增强后减弱,γ织构先减弱后增强,α织构稍有弱化。冷轧过程中形变储能累积具有明显的初始取向依赖性,初始γ取向储能累积速率在低于50%压下率时与初始α取向接近,高于50%压下率时则明显大于后者,初始λ取向储能累积速率始终显著低于γ和α取向,转至同一形变取向的不同初始取向间的储能累积也会产生差异。冷轧过程中不同初始织构组分的取向流动与形变储能累积规律,决定了无取向硅钢再结晶织构组分的发展。     

Influence of crystallographic textures on tensile properties of 316L austenitic stainless steel

Role of cold rolling texture on the tensile properties of the cold rolled and cold rolled and annealed AISI 316L austenitic stainless steel is described here. The solution-annealed stainless steel plates were unidirectionally cold rolled to 50, 70 and 90% of reduction in thickness. The cold rolled material was annealed at 500–900 °C annealing temperatures. X-ray diffraction technique was employed to study the texture evolution in cold rolled as well as cold rolled and annealed conditions. The texture components that evolved were translated into slip transmission number ‘λ’ and Schmid factor ‘μ’. These two parameters were correlated with the tensile properties of the material. The tensile properties were evaluated under all processing conditions. Softening of the cold rolled material was observed after annealing with increasing annealing temperatures. From the stress–strain curves, strain hardening coefficient ‘n’ and strain hardening rate ‘θ’ were determined. It was found that the effect of texture on tensile behaviour could be understood clearly by strain hardening rate. Out of the two parameters, ‘n’ and ‘θ’, strain hardening rate was found to be more sensitive to type of texture in the material.     

Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

An analytical study is carried out on the elastic–plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material is thought of as obeying an elastic-perfectly-plastic or a strain hardening law. When the notch root radius becomes zero, the analytical frame matches the solutions for the crack case due to Hult–McClintock (elastic-perfectly-plastic material) and Rice (strain hardening material). The analytical frame provides an explicit link between the plastic stress and the elastic stress at the notch tip. Neuber’solution for blunt notches under antiplane shear is also obtained and the conditions under which such a solution is valid are discussed in detail by using elastic and plastic notch stress intensity factors. Finally, revisiting Glinka and Molski’s equivalent strain energy density (ESED), these factors are used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case.     

Analysis of crack tip plasticity for microstructurally small cracks using crystal plasticity theory

Crack tip plastic zone sizes and crack tip opening displacements (CTOD) for stationary microstructurally small cracks are calculated using the finite element method. To simulate the plastic deformation occurring at the crack tip, a two-dimensional small strain constitutive relationship from single crystal plasticity theory is implemented in the finite element code ANSYS as a user-defined plasticity subroutine. Small cracks are modeled in both single grains and multiple grains, and different crystallographic conditions are considered. The computed plastic zone sizes and CTOD are compared with those found using conventional isotropic plasticity theory, and significant differences are observed.     

Crystallography-based prediction of plastic anisotropy of polycrystalline materials

The on-line prediction of metal sheet formability requires that both material characterization (texture identification) and yield loci predetermination be done in very shor time intervals. Of two applicable approaches, i.e., continuum mechanics and crystallography-based methods, only the latter are suitable for this purpose. Several models of plasticity of a polycrystalline material were reviewed, and their applicability to the prediction of plastic anisotropy of face-centered cubic (FCC) metals was evaluated. A tailored set of cold-rolled copper alloy samples was designed and manufactured, representing the wide spectrum of textures and cold work levels typical for the sheet metal industry. The texture was quantitatively described in the form of the orientation distribution functions derived by the inversion of four incomplete pole figures. The Taylor-Bishop-Hill model was applied in order to calculate the planar variation of the plastic strain ratio. The continuum mechanics of textured polycrystals approach was also used for the prediction of the plastic strain-rate ratio for the same set of deformed materials. The theoretical predictions were compared with the plastic strain ratios measured in tensile tests using strain gauges. The applicability of the models for prediction of the plastic anisotropy of FCC metals was discussed in view of the operating deformation mechanisms and other factors such as strain hardening sensitivity and grain size/shape effects.     

Study of Deformation Mechanisms in Titanium by Interrupted Rolling and Channel Die Compression Tests

The mechanisms of small plastic deformation of titanium (T40) during cold rolling and channel die compression by means of "interrupted in situ" EBSD orientation measurements were studied. These interrupted EBSD orientation measurements allow to determine the rotation flow field which leads to the development of the crystallographic texture during the plastic deformation. Results show that during rolling, tension twins and compression twins occur and various glide systems are activated, the number of grains being larger with twins than with slip traces. In channel die compression, only tension twins are observed in some grains, whereas slip traces can be spotted in almost all observed grains. The different stress conditions and different strain rates existing under the two modes of deformation lead to the activation of different deformation mechanisms.     

罩式退火无间隙原子钢的最优冷轧压下率的确定

以工业生产的含钛、铌和含钛的两种无间隙原子(IF)钢热轧钢板为试验材料,在实验室研究了冷轧压下率对两种IF钢的显微组织、力学性能和再结晶织构的影响。结果表明:在试验条件下,两种试验钢经不同冷轧压下率冷轧和720℃×5 h罩式退火后,再结晶完成,随着冷轧压下率的增加,晶粒变得细小均匀,退火后得到的织构也增强,并且织构类型有转向{111}织构的趋势;塑性应变比r90在压下率为70%时达到最大值,随着冷轧压下率的进一步增大,r90值减小;应变硬化指数n90值逐渐降低。最后提出工业生产中冷轧压下率最佳范围为70%~80%,可获得良好的深冲性能。     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.     

The Equivalent Strain Energy Density approach re-formulated and applied to sharp V-shaped notches under localized and generalized plasticity

In the case of a rounded notch, the stress and strain at the notch tip can be determined by the traditional Neuber rule or by the Equivalent Strain Energy Density (ESED) approach, as formulated by Glinka and Molski. In the latter case the elastoplastic strain energy density at the notch tip is thought of as coincident with that determined under purely elastic conditions. For sharply V‐shaped notches this approach is not directly applicable, since the strain energy density at the notch tip tends toward infinity both for a material obeying an elastic law and a material obeying a power hardening law. By using the notch stress intensity factors, the present paper suggests a re‐formulation of the ESED approach which is applied no longer at the notch tip but to a finite size circular sector surrounding the notch tip. In particular we have adopted the hypothesis that, under plane strain conditions, the value of the energy concentration due to the notch is constant and independent of the two constitutive laws. When small scale yielding conditions are present, such a hypothesis immediately results in the constancy of the strain energy averaged over the process volume. As a consequence, plastic notch stress intensity factors valid for sharp V‐shaped notches can be predicted on the basis of the linear elastic stress distributions alone.     

MECHANICAL REASONS FOR PLASTICITY-INDUCED CRACK CLOSURE UNDER PLANE STRAIN CONDITIONS

A mechanical explanation of plasticity-induced crack closure under plain strain conditions is given first by means of dislocation mechanics and then by the methods of continuum mechanics. In plane strain, the event of crack closure is due to transport of material from the wake to the crack tip. It is an elastic effect caused by the response of the matrix surrounding the plastic wake. The transported material produces a wedge which follows the crack tip, and unlike the plane stress condition it does not leave a remaining layer on the crack flanks. The length of the produced wedge at the crack tip is of the same scale as the plastic zone. It is then shown that in spite of its smallness this wedge is able to cause the experimentally observed shielding effect. The results also suggest that the discrepancies concerning the interpretation of fatigue crack growth and closure experiments are likely to be due to differences in accuracy in the detection of such small but nevertheless effective wedges.     

Transient effect on ideally plastic stationary crack tip fields

This paper analyses the transient effect on ideally plastic stationary crack tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems of ideally plastic stationary crack tip fields when the inertial forces are not negligible.     

Texture evolution in equal-channel angular extrusion

The focus of this article is texture development in metals of fcc, bcc, and hcp crystal structure processed by a severe plastic deformation (SPD) technique called equal-channel angular extrusion (ECAE) or equal-channel angular pressing (ECAP). The ECAE process involves very large plastic strains and is well known for its ability to refine the grain size of a polycrystalline metal to submicron or even nano-size lengthscales depending on the material. During this process, the texture also changes substantially. While the strength, microstructure and formability of ECAE-deformed metals have received much attention, texture evolution and its connection with these properties have not. In this article, we cover a multitude of factors that can influence texture evolution, such as applied strain path, die geometry, processing conditions, deformation inhomogeneities, accumulated strain, crystal structure, material plastic behavior, initial texture, dynamic recrystallization, substructure, and deformation twinning. We evaluate current constitutive models for texture evolution based on the physics they include and their agreement with measurements. Last, we discuss the influence of texture on post-processed mechanical response, plastic anisotropy, and grain refinement, properties which have made ECAE, as well as other SPD processes, attractive. It is our intent to make SPD researchers aware of the importance of texture development in SPD and provide the background, guidance, and methodologies necessary for incorporating texture analyses in their studies.     

The anisotropic R-criterion for crack initiation

The anisotropic nature of mixed modes I-II crack tip plastic core region and crack initiation is investigated in this study using an angled crack plate problem under various loading conditions. Hill’s anisotropic yield criterion along with singular elastic stress field at the crack tip is employed to obtain the non-dimensional variable-radius crack tip plastic core region. In addition, the R-criterion for crack initiation proposed by the authors for isotropic materials is also extended to include anisotropy. The effect of Hill’s anisotropic constants on the shape and size of the crack tip plastic core region and crack initiation angle is presented for both plane stress and plane strain conditions at the crack tip. The study shows a significant effect of anisotropy on the crack tip core region and crack initiation angle and calls for further development of anisotropic crack initiation theory.     

Effect of cold rolling on plastic deformation and microstructure of bearing ring

Bearing ring blanks of the high-speed rail bearings, machine tool spindle bearings and wind power bearings have been manufactured through the ring rolling technology. Yet, the microstructure evolution of bearing ring in cold ring rolling remains unclear. In this work, the plastic strain distribution of the rolled ring is first simulated. Then, the microstructure of bearing ring is studied by the electron backscatter diffraction technique. Furthermore, the microstructure changes in cold ring rolling are investigated through band contrast images, and the texture evolutions after various deformation ratios are analysed by the technique of 3D-Euler space distribution. This work provides valuable guidelines for enhanced understanding the role of the cold ring rolling technology on the microstructure evolution of bearing rings.     

Study of hardening and cyclic plastic behaviour around the crack tip of C(T) specimen made by as‐received and annealed copper

The purpose of this research is determining experimentally the characteristics of tension and cyclic plastic behaviours of as‐received and annealed coppers and studying distribution of stress/strain field near the crack tip. Samples made by pure copper were annealed at 420°C for 40 minutes in electric furnace. To determine the properties of the cyclic plastic behaviour, proper tests with symmetric strain‐controlled conditions were performed on standard samples. Chaboche nonlinear hardening model was used to determine the cyclic plastic behaviour of both materials. According to results, annealing process creates isotropic hardening in the copper and also changes its initial kinematic hardening behaviour. Effects of the annealing and hardening on the variations of the stresses and strains around the crack tip were investigated. Also, ratcheting and mean stress relaxations versus number of cycles, inside the plastic region, were studied.     

An interface crack in a coating-substrate composite with mixed-mode Dugdale corrections

Considering both plane stress and plane strain conditions, the plastic zone size and the crack tip opening displacement of an interface crack between a coating and a semi-infinite substrate under a normal load on the crack surfaces are investigated by the mixed-mode Dugdale model. In the model, stresses applied in the plastic zones satisfy the Von Mises yield criterion. The plastic zone size can be calculated by satisfying the condition that the complex stress intensity factors vanish. After the plastic zone size is solved, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, a uniform load is considered, and the effects of the normalized elastic modulus (the ratio of the elastic modulus of the coating to the elastic modulus of the substrate) and the normalized crack depth (the ratio of the coating thickness to the interface crack length) on the normalized plastic zone size and the normalized crack tip opening displacement are examined. Numerical examples show in the case of thin coatings, the value of the normalized plastic zone size decreases with increasing the normalized elastic modulus.     

Influence of crack tip constraint on void growth in pressure sensitive plastic solids - I: 2D analysis

In this work, the effect of constraint on void growth near a notch tip under mode-I loading is investigated in materials exhibiting pressure sensitive yielding and plastic dilatancy. To this end, large deformation elastic-plastic finite element analyses are performed using a two-dimensional (2D) plane strain, modified boundary layer formulation by prescribing the elastic K − T field as remote boundary conditions. The analyses are conducted for different values of K (or J) and T-stress. The material is assumed to obey a finite strain, Extended Drucker-Prager yield condition. The roles of pressure sensitivity, plastic dilatancy and yield locus shape on the interaction between the notch and a nearby void are studied by examining the distribution of hydrostatic stress and plastic strain in the ligament connecting them as well as the growth of notch and the void. The results show that void growth with respect to J is enhanced due to pressure sensitivity, and more so when the plastic flow is non-dilatational. By contrast, irrespective of pressure sensitivity, loss of crack tip constraint can significantly retard void growth.