Papers by Author: X.B. Wang

Abstract: The coexistent phenomenon of deformed and transformed adiabatic shear bands (ASBs) is analyzed using Johnson-Cook model and gradient-dependent plasticity for heterogeneous ductile metal material. The size of deformed ASB is described by the internal length reflecting the heterogeneity of material. Microstructural effect leads to a nonuniform distribution of temperature rise in deformed ASB. When the peak temperature in deformed ASB exceeds the transformation temperature, a transformed ASB appears at the center of deformed ASB. With a decrease of flow shear stress, the width of transformed ASB increases until its upper bound, i.e., the size of deformed ASB, is reached. The effects of initial temperature and strain rate on the occurrence of transformation, evolution of the thickness of transformed ASB, distributions of local temperature and plastic shear deformation in ASB are investigated. Lower initial temperature results in higher peak shear stress, later occurrence of shear strain localization, lower shear stress when transformation occurs, later occurrence of transformation, thinner transformed ASB, lower peak temperature in ASB, and lower value of local plastic shear deformation in the boundaries of transformed ASB. At higher strain rates, the transformed ASB is wider; the peak temperature in ASB is higher; the value of local plastic shear deformation in the boundaries of transformed ASB is higher; the flow shear stress that corresponds to transformation is higher; earlier occurrence of transformation and higher peak shear stress will be expected.

Abstract: For many quasi-brittle materials (such as rock, ceramic and concrete) in pure bending state, the material on the tensile side will fail firstly since the compressive strength can be ten times the tensile strength. After tensile strain localization zone is initiated in the midspan of the beam, its propagation direction will be perpendicular to the neutral axis. In the paper, using nonlocal theory or gradient-dependent plasticity, the distributions of local plastic tensile strain and local damage variable in tensile strain localization zone of a pure bending beam are analyzed theoretically. The evolutions of the maximum local plastic tensile strain, the maximum local damage variable and the bending moment with tensile stress acting on the tensile side are presented through examples. The distributions of local plastic tensile strain and local damage variable in tensile strain localization zone are highly nonuniform due to microstructural effect. When the maximum bending moment is reached, the maximum local damage variable is proportional to the ratio of elastic modulus to elastoplastic modulus, while the maximum local plastic tensile strain is inversely proportional to elastic modulus and elastoplastic modulus. For quasi-brittle materials, the elastoplastic modulus that is a constitutive parameter equal to the absolute value of the slope of tensile stress-tensile strain curve in strain-softening stage is much higher. The present theoretical results mean that the precursors to failure are less apparent for extremely brittle materials.

Abstract: The failure process of heterogeneous rock specimen with initially random material imperfections in uniaxial plane strain compression and the macroscopically mechanical response are numerically modeled by using FLAC (Fast Lagrangian Analysis of Continua). A FISH function is generated to prescribe the initial imperfections within the heterogeneous specimen by using Matlab. The imperfection is weaker than the intact rock. Beyond the failure of the imperfection, it undergoes ideal plastic behavior, while intact rock exhibits linear strain-softening behavior and then ideal plastic behavior once failure occurs. The specimen with smooth ends is loaded at a constant strain rate and is divided into 3200 elements. The maximum numbers of the initial imperfections in five schemes are 100, 300, 500, 700 and 900. The effects of the number of the imperfections on the fracture process, the final fracture pattern and the complete stress-strain curve are investigated. Prior to the peak stress, some imperfections extend in the axial direction and then a part of them coalesce to form inclined shear bands. Beyond the peak stress, shear bands progressively intersect the specimen; in the process the number of the yielded elements approximately remains a constant. With an increase of the number of the initial imperfections, the spacing of shear fractures decreases, the peak stress and corresponding axial strain decrease; the post-peak branch of stress-strain curve becomes steeper; much more elements fail in tension; the number of the yielded elements in tension in the vicinity of the two lateral edges of the specimen remarkably increases.

Abstract: Effects of joint width (JW) on the macroscopic stress-strain curve, the failure process and mode of jointed rock specimen (JRS) in plane strain compression are modeled by use of FLAC. The failure criterion of intact rock outside the inclined joint is a composite Mohr-Coulomb criterion with tension cut-off and the linear strain-softening post-peak constitutive relation is adopted. The joint is treated as quadrate elements of ideal plastic material beyond the peak strength. A written FISH function is used to automatically find elements in the joint. Numerical results show that the peak strength of JRS depends on JW and is lower than that of intact rock specimen without joint. For JRS, the shear strains are concentrated into the joint or the new generated shear bands (NGSBs); the peak strength decreases with an increase of JW. At lower or higher joint inclination angle (JIA), the failure mode and pattern of NGSBs are not related to JW. The post-peak response becomes ductile at wider JW and higher JIA. The post-peak slope of stress-strain curve at lower JIA is not dependent on JW since the width and inclination angle of NGSBs are not affected by JW.

Abstract: Gradient-dependent plasticity considering the microstructural effect is introduced into Johnson-Cook model to calculate the nonuniform temperature distribution in adiabatic shear band (ASB) and the evolutions of average and peak temperatures in ASB. Effects of initial static yield stress, strain-hardening coefficient, strain-hardening exponent, strain-rate parameter and thermal-softening parameter are numerically investigated. The calculated peak temperature in ASB considering both the plastic work and the microstructural effect is always greater than the average temperature calculated only using the plastic work. For much lower flow shear stress, the peak temperature approaches two times the average temperature. The occurrence of phase transformation in ASB is easier in metal material with higher initial static yield stress, strain-hardening coefficient, strain-rate parameter and thermal-softening parameter. At much lower flow shear stress or much higher average plastic shear strain, the phase transformation occurs more easily in material with a lower strain-hardening exponent. Traditional elastoplastic theory without the microstructural effect underestimates the peak temperature in ASB so that the experimentally observed phase transformations cannot be explained.

Abstract: The stress distribution on the midsection of a pure bending beam where tensile strain localization band initiates on the tensile side of the beam and propagates within the beam is analyzed. Using the static equilibrium condition on the section of the midspan of the beam and the assumption of plane section as well as the linear softening constitutive relation beyond the tensile strength, the expressions for the length of tensile strain localization band and the distance from the tip of the band to the neutral axis are derived. After superimposing a linear unloading stress distribution over the initial stress distribution, the residual stress distribution on the midsection of the beam is investigated. In the process of strain localization band’s propagation, strain-softening behavior of the band occurs and neutral axis will shift. When the unloading moment is lower, the length of tensile strain localization band remains a constant since the stress on the base side of the beam is tensile stress. While, for larger unloading moment, with an increase of unloading moment, the length of tensile strain localization band decreases and the distance from the initial neutral axis to the unloading neutral axis increases. The neutral axis of midsection of the beam will shift in the unloading process. The present analysis is applicable to some metal materials and many quasi-brittle geomaterials (rocks and concrete, etc) in which tensile strength is lower than compressive strength. The present investigation is limited to the case of no real crack. Moreover, the present investigation is limited to the case that the length of strain localization band before unloading is less than half of depth of the beam. Otherwise, the residual tensile stress above the elastic neutral axis will be greater than the tensile strength, leading to the further development of tensile strain localization band in the unloading process.

Abstract: Gradient-dependent plasticity where a characteristic length is involved to consider the microstructural effect (interactions and interplaying among microstructures due to the heterogeneous texture) and the measured nonlinear shear stress-shear strain curves for different loading strain rates are used to calculate the distribution of local temperature rise in adiabatic shear band (ASB) for aluminum-lithium alloy specimen of thin-walled tube in dynamic torsion test. ASB is assumed to initiate just at peak shear stress in the specimen. The temperature rise in ASB is decomposed into the uniform temperature rise in strain-hardening stage and the nonuniform temperature rise in strain-softening stage. The former depends on the measured nonlinear shear stress-shear strain curve prior to the peak, the density, the work to heat conversion factor and the heat capacity. The latter is related to the softening branch of the measured nonlinear shear stress-shear strain curve, the internal length parameter and the physical parameters. For binary Al-Li alloy, the predicted maximum temperatures in ASB are 413K at strain rate of 2000s-1 and 433K at strain rate of 2600s-1. These peak temperatures are lower than the recrystallization and phase transformation temperatures. Higher loading strain rate results in higher pre-peak and post-peak temperature rises, steeper profile of local temperature and higher peak local temperature in ASB. These predictions qualitatively agree with the previously analytical solution for ductile metal exhibiting linear strain-softening behavior beyond the peak shear stress based on gradient-dependent plasticity.

Abstract: Gradient-dependent plasticity where a characteristic length is involved to consider the microstructural effect (interactions and interplaying among microstructures due to the heterogeneous texture) is introduced into Zerilli-Armstrong model based on the framework of thermally activated dislocation motion. Effect of initial temperature on the distributions of plastic shear strain and deformation in adiabatic shear band (ASB), the axial compressive stress-axial compressive strain curve, the shear stress-average plastic shear strain in ASB curve and the plastic shear strain corresponding to the occurrence of shear strain localization is investigated. The axial deformation within aluminum-lithium alloy specimen in uniaxial compression in strain-hardening stage is considered to be uniform. Beyond the peak compressive stress, a single ASB with a certain thickness determined by internal length is formed and intersects the specimen. The axial plastic deformation is decomposed into uniform deformation and localized deformation due to the shear slip along ASB. Lower temperature leads to earlier occurrence of shear strain localization, i.e., lower critical plastic compressive strain, steeper post-peak shear stress-average plastic shear strain in ASB curve, higher peak shear stress and more apparent shear strain localization. The calculated distributions of plastic shear strain and deformation in ASB are highly nonuniform due to the microstructural effect, as cannot be predicted by classical elastoplastic theory applicable to completely homogenous material. The predicted average plastic shear strains in ASB for different widths of ASB agree with the measured values for under-aged Al-Li alloy at 298K and at strain rate of approximately 103s-1.

Abstract: Gradient-dependent plasticity where a characteristic length is involved into yield function is adopted to calculate the thickness of shear band (SB) and the distribution of plastic shear strain in SB. The characteristic length reflecting the heterogeneous extent of texture only controls SB’s thickness. The local plastic shear strain in SB is highly non-uniform. The total fracture energy is the sum of pre-peak and post-peak fracture energies. The pre-peak part is described by the nonlinear Scott model and depends on the height of specimen. The post-peak part is calculated through the derived post-peak relative stress-plastic deformation curve. If the inclination angle of SB is not influenced by the height, then the slope of post-peak relative stress-plastic deformation curve and the post-peak fracture energy are independent of the height. The total fracture energy is linearly size-dependent as the pre-peak fracture energy is linearly related to the height. The slope of postpeak relative stress-plastic deformation and the total fracture energy are verified through previous experiments for normal concrete in uniaxial ompression.

Abstract: Gradient-dependent plasticity where a characteristic length is involved to consider the microstructural effect (interactions and interplaying among microstructures due to the heterogeneous texture) is introduced into Johnson-Cook model considering the effects of strain-hardening, thermal softening and strain rate sensitivity. Effects of initial static yield stress, strain-hardening coefficient and exponent, strain-rate and thermal-softening parameters on the occurrence of phase transformation and the thickness of phase transformed adiabatic shear band (ASB) in deformed ASB are numerically investigated. Higher initial static yield stress, strain-hardening coefficient, strain-rate parameter and lower strain-hardening exponent lead to earlier occurrence of phase transformation (lower plastic shear strain). Effect of thermal-softening parameter on plastic shear strain corresponding to the onset of phase transformation is not monotonous. Transformed ASB is located at the center of deformed ASB since the position has higher temperature exceeding the temperature of phase transformation. The thickness of transformed ASB increases with decreasing flow shear stress and the increasing tendency becomes slow. For the same flow shear stress, the thickness of transformed ASB is wider for higher initial static yield stress, strain-hardening coefficient and exponent, strain-rate and thermal-softening parameters. Compared with classical elastoplastic theory applicable to completely homogenous material, gradient-dependent plasticity considering the microstructural effect predicts that phase transformation occurs earlier and that the thickness of transformed ASB changes with flow shear stress.