Numerical investigation of dynamic shear bands in inelastic solids as a problem of mesomechanics

The main objective of the present paper is to discuss very efficient procedure of the numerical investigation of the propagation of shear band in inelastic solids generated by impact-loaded adiabatic processes. This procedure of investigation is based on utilization the finite element method and ABAQUS system for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic polycrystalline solids with a finite set of internal state variables is used. The set of internal state variables is restricted to only one scalar, namely equivalent inelastic deformation. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena. As a numerical example we consider dynamic shear band propagation in an asymmetrically impact-loaded prenotched thin plate. The impact loading is simulated by a velocity boundary condition, which are the results of dynamic contact problem. The separation of the projectile from the specimen, resulting from wave reflections within the projectile and the specimen, occurs in the phenomenon. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Shear band advance, shear band velocity and the development of the temperature field as a function of time have been determined. Qualitative comparison of numerical results with experimental observation data has been presented. The numerical results obtained have proven the usefulness of the thermo-elasto-viscoplastic theory in the investigation of dynamic shear band propagations.     

On pressure-shear plate impact for studying the kinetics of stress-induced phase transformations

Pressure-shear plate impact experiments are proposed for studying the kinetics of stress-induced phase transformations. The purpose of this paper is to determine loading conditions and specimen orientations which can be expected to activate a single habit plane variant parallel to the impact plane, thereby simplifying the study of the kinetics of the transformation through monitoring the wave profiles associated with the propagating phase boundary. The Wechsler-Lieberman-Read phenomenological theory was used to determine habit plane indices and directions of shape deformation for a Cu---Al---Ni shape memory alloy which undergoes a martensitic phase transformation under stress. Elastic waves generated by pressure-shear impact were analyzed for wave propagation in the direction of the normal to a habit plane. A critical resolved shear stress criterion was used to predict variants which are expected to be activated for a range of impact velocities and relative magnitudes of the normal and transverse components of the impact velocity.     

冲击压缩下氧化铝陶瓷中的延迟破坏实验研究

利用轻气炮对不同厚度的氧化铝陶瓷试件进行了平板冲击实验,并借助激光速度干涉仪(VISAR)测试了试件的自由面速度历程。实验结果显示,自由面速度曲线上存在表征破坏波出现的二次压缩信号。根据实验结果计算获得了破坏波穿过试件的运动进程,并确定了试件中破坏波的运动轨迹近似为一条直线,得出在冲击压力为7.16GPa时试件内破坏波波速约为5.051km/s,破坏延迟时间约为0.105μs。最后简单分析了该现象产生的物理机制。     

The effects of plastic deformation on stress wave propagation in multi-layer materials

The behavior of a multi-layer material at high strain rate and the effect of plastic deformation on stress wave propagation were investigated by a combination of experimental and numerical techniques. Plastic deformation effects were studied in multi-layer materials consisting of ceramic, copper and aluminum subjected to large strains under high strain rate loading. First, stress wave propagation behavior for the monolithic metals was studied, and then extended to multilayer combinations of these metals with each other and with a ceramic layer. The axial stress distributions were found to be non-uniform in the elastic deformation range of the specimen. The degree of non-uniformity was much more pronounced in the multi-layer samples consisting of different materials. The presence of a ceramic layer increased the magnitudes of stress gradients at the interfaces. It was also found that a major effect of plastic deformation is a tendency to produce a more homogeneous stress distribution within the components. The implications of these observations for practical systems are discussed.     

Deformation characteristics of low carbon steel subjected to dynamic impact loading

The effects of impact loading on changes in microstructure have been studied in low carbon steel. Low to moderate shock loading tests have been carried out on steel specimens using a single stage gas gun with projectile velocities ranging from 200 to 500 m/s. Stress history at the back face of the target specimen and projectile velocity prior to impact were recorded via manganin stress gauges and velocity lasers, respectively. A Johnson-Cook constitutive material model was employed to numerically simulate the material behavior of low carbon steel during impact and obtain the particle velocity at the impact surface as well the pressure distribution across the specimens as a function of impact duration. An analytical approach was used to determine the twin volume fraction as a function of blast loading. The amount of twinning within the α-ferrite phase was measured in post-impact specimens. A comparison between experimental and numerical stress histories, and analytical and experimental twin volume fraction were used to optimize the material and deformation models and establish a correlation between impact pressure and deformation response of the steel under examination. Strain rate controlled tensile tests were carried out on post-impact specimens. Results of these tests are discussed in relation to the effects of impact loading on the yield and ultimate tensile strength as well as the hardening and strain energy characteristics.     

On the impact of the time increment on sensitivity analysis during the elastic-to-viscoplastic transition in metals

In many constitutive models of elasto- viscoplasticity, like for example overstress models, viscoplastic deformation takes place once the stress state lies outside the yield surface. In most computational implementations of such constitutive laws, the calculation of the viscoplastic deformation increment is performed in a one-step approach by applying the full nominal time increment to the rate-dependent deformation, even if during a part of the increment, purely elastic deformation takes place. This way, time increments affected by the transition from elastic to viscoplastic material behaviour are not properly accounted for, because such time increments exhibit both a purely elastic part and a elastoviscoplastic part. In fact, it has been reported in the literature that errors induced by the use of the conventional one-step approach are insignificant. In the present article, the impact of using the one-step approach, i.e. using the total time increment in case of the elastic-to-viscoplastic transition, on sensitivity analysis is investigated.     

Localized fracture phenomena in thermo-visco-plastic flow processes under cyclic dynamic loadings

Summary The main objective of the paper is the investigation of localized fatigue fracture phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings. Recent experimental observations for cycle fatigue damage mechanics at high temperature and dynamic loadings of metals suggest that the intrinsic microdamage process does very much depend on the strain rate and the wave shape effects and is mostly developed in the regions where the plastic deformation is localized. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history dependent, nonlinear process.A general constitutive model of elasto-viscoplastic damaged polycrystalline solids developed within the thermodynamic framework of the rate type covariance structure with a finite set of the internal state variables is used (cf. Dornowski and Perzyna [16], [17], [18]). A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic nonnormality; (ii) plastic strain induced anisotropy (kinematic hardening); (iii) softening generated by microdamage mechanisms (nucleation, growth and coalescence of microcracks); (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity; (vi) plastic spin.To describe suitably the time and temperature dependent effects observed experimentally and the accumulation of the plastic deformation and damage during a dynamic cyclic loading process the kinetics of microdamage and the kinematic hardening law have been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elasticplastic response can be obtained. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite difference method. Particular attention is focussed on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. The Lax-Richtmyer equivalence theorem is formulated, and conditions under which this theory is valid are examined. Utilizing the finite difference method for a regularized elasto-viscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body under cyclic loading condition is presented.Particular examples have been considered, namely a dynamic adiabatic cyclic loading process for a thin plate with sharp notch. To the upper edge of the plate is applied a cyclic constraint realized by rigid rotation of the edge of the plate while the lower edge is supported rigidly. A small localized region, distributed asymmetrically near the tip of the notch, which undergoes significant deformation and temperature rise, has been determined. Its evolution until occurrence of fatigue fracture has been simulated.The propagation of the macroscopic fatigue damage crack within the material of the plate is investigated. It has been found that the length of the macroscopic fatigue damage crack distinctly depends on the wave shape of the assumed loading cycle.     

面板堆石坝震动响应及变形规律的试验研究

采用Parkfield波作为地震动输入,在清华大学50g-t土工离心机振动台上中进行了一组面板堆石坝动力离心模型试验。试验在50倍重力加速度条件下完成,采用加速度传感器测量了模型不同位置动力响应的加速度时程并且采用应变片测量了面板的应力-应变,通过改变地震波输入的幅值和是否蓄水分析研究了面板堆石坝的震动响应及变形规律。结果表明面板坝自下而上存在地震响应放大现象,靠近上下游坝坡位置的加速度响应要大于同高程处坝轴线附近的加速度响应;地震作用下面板产生较明显的压应力,最值发生在面板中上部;面板中部出现较明显的弯矩;改变输入地震波的幅值大小对坝体加速度响应的分布规律、坝体位移变化的分布规律以及面板应力变形的分布规律没有影响,但地震波输入幅值的增加会减弱地震波的加速度放大效应;竣工期的地震加速度响应比蓄水期的要大,说明蓄水可以削弱地震波对坝体的加速度响应,但蓄水会导致坝体和面板的变形增加。     

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are investigated.     

Development of viscoplastic strains during creep in continuous fibre GMT composites

This work is part of a larger study aimed at characterizing the viscoelastic–viscoplastic behavior of a continuous fiber glass mat thermoplastic composite. The purpose of this paper is to experimentally and numerically decouple the viscoplastic strains from total creep response. This enabled the characterization of the evolution of viscoplastic strains as a function of time, stress and loading cycles. The separation also allowed viscoplastic strain development to be corresponded with the progression of failure mechanisms such as interfacial debonding and matrix cracking which were captured in situ. This was achieved by performing creep tests at seven stress levels between 20 and 80 MPa. For each stress level, a series of creep-recovery tests were performed on single specimen for increasingly longer durations from 1 to 24 h. Stress and time dependence of viscoplastic strains were determined experimentally. Using part of the data generated, a viscoplastic model was developed following a method proposed by Nordin. The model had excellent agreement with experimental results for all stresses and times considered. In multiple loading cycles, the viscoplastic strain development is accelerated with increasing number of cycles at higher stress levels. The results further verify the technique for numerical separation of viscoplastic strains proposed in an earlier work. Finally, it was found that the development viscoelastic strains during creep are affected by the previous viscoplastic strain history.     

SHPB冲击压缩实验中泡沫塑料应力均匀化过程的数值模拟

对SHPB实验中泡沫塑料的本构关系进行了分段线性化处理，基于一维弹性应力波理论用数值方法对变形过程进行了模拟。结果表明，实验初期试件处于严重的应力不均匀状态；并且由于试件与输入／输出杆的界面处存在波阻抗不匹配现象，实验中后期的应力均匀化程度也无法得到有效提高；若将子弹及输入／输出杆的材料更换为刚度较低的聚合物，可有效地减少波阻抗不匹配的程度，从而使实验中后期的应力均匀化水平得以大幅度提高，但实验所能够达到的最大应变值可能受到限制。     

An experimental method to validate viscoplastic constitutive equations in the dynamic response of plates

In the present paper measured and simulated vibrations of viscoplastic plates under impulsive loadings are compared to each other. The aim is to determine how accurately the measured deformations can be calculated by the chosen constitutive and structural theories. A first-order shear deformation shell theory assuming small strains and moderate rotations as well as viscoplastic laws are used. In the experimental part of this study short time measurement techniques are applied to shock tubes in order to record fast loading processes and plate deformations.     

Simulation of deformation and lifetime behavior of a fcc single crystal superalloy at high temperature under low-cycle fatigue loading

This work deals with the formulation of a three-dimensional crystallographic time-incremental lifetime rule for face-centered cubic (fcc) single crystals used for gas-turbine blade applications. The damage contribution rate of each slip system to the total damage is governed by the current values of the resolved shear stress and the slip rate on the corresponding slip system. The damage rule is combined with a crystallographic viscoplastic deformation model. For the nickel-base single-crystal superalloy CMSX4 at 950 °C, various strain- and stress-controlled uniaxial cyclic tests with and without hold-times can be described for different crystal orientations by one set of material parameters. For verification, simulation results for a single-crystal specimen with a notch have been compared with corresponding experimental results. The predicted lifetime is within the factor of two of the measured one.     

Modelling impact deformation of foam-plate sandwich systems

Foam-plate sandwich systems comprising ten layers of crushable polyurethane foam separated by mild steel plate inserts are subjected to impact deformation at velocities ranging from 3 to 8 m/s using a drop tower. Four geometrical arrangements, namely uniform-width, tapered-width, hourglass and double tapered-width profiles, are studied to identify the effects of varying the distribution of structural compliance and inertia on impact response. The investigations focuses on the force transmitted through the sandwich systems and the development of deformation. A one-dimensional mass-spring chain model is formulated to describe the observations. Both theoretical and experimental results indicate that the systems geometry has a significant influence on the development and distribution of deformation and consequently, the force-time response. The theoretical model provides reasonable predictions of the final damage distribution in each system and good correlation is observed between the theoretical and experimental transmitted force response in terms of overall behaviour. In essence, the study shows how the impact force transmitted by an energy-dissipating system can be controlled by manipulating the distribution of inertia and compliance within the system.     

Effect of interlayer on stress wave propagation in CMC/RHA multi-layered structure

Due to the significance of the propagation of stress wave in composite armor during projectile–target interaction, the characteristics of stress wave propagation in multi-layered composite structure under impact load were investigated by traditional Split Hopkinson Pressure Bar system in this study. The effect of interlayer characteristic on the stress wave propagation was discussed. The results show that the interlayer properties between CMC and RHA steel play an important role in the propagation of wave. Compared to “CMC/RHA” structure without interlayer, the tungsten carbide interlayer can increase stress level in CMC layer remarkably, while silica gel layer has an opposite effect, and epoxy resin adhesive layer has no distinct effect on the propagation of stress wave. The increased compressive stress level in CMC layer is very useful when the CMC layer served as the face plate of a composite armor. During the impact process of the projectile to the armor, the anti-penetration capability of the face plate of the composite armor can be improved when in the compression stress state. In the comparison ballistic testing conducted with 7.62 mm armor piercing projectiles, the protection efficiency of the “CMC/WC/RHA” composite armor is about 36% higher than that of the “CMC/RHA” structure, which is in good correlation with the stress wave measurement results.     

Time resolved plastic deformations in rods subjected to transverse impact

This paper describes experiments to record deformation profiles versus time in metallic rods subjected to transverse ballistic impacts. Rod materials included a tungsten alloy, four alloys of steel, titanium, and copper. The deformation profiles were analyzed to determine time resolved transverse plastic deformation wave speeds in all the rod materials and to estimate effective fracture shear strains in some of the materials. These material parameters are key elements in an analytical model to estimate deformations and failure in long rod penetrators subjected to transverse loads arising from non-ideal plate penetration geometries (yaw and obliquity). The rod materials were also subjected to tensile tests and Taylor anvil impact tests to measure static tensile and dynamic compressive strengths and longitudinal plastic wave speeds. The Taylor anvil and transverse rod impact tests together furnish the required dynamic material properties for comparing the penetration effectiveness of candidate rod materials and geometries.     

Preliminary experiments in acoustoelastic responses of a plastically deformed solid

Abstract

In this paper, the details of the experimental techniques and set‐ups needed in the acoustic birefringence measurement are given. To precisely determine the wave speeds, the Echo‐Overlap method with reflection mode is adopted. The details of the fabrication of a dual‐polarization ultrasonic shear‐wave transducer are also included. The anelastic effect which occurs in the acoustoelastic measurement of a plastically deformed steel (C1018) specimen is examined. The general assumption of slight orthotropy which is used in ultrasonic stress measurement of polycrystalline metal is tested. The annealing experiment shows that the preferred orientation of the cold‐rolled steel plate can not be changed by annealing the specimen at the recovery temperature. The measurement of the third order elastic constants of the steel specimen is also conducted.     

A nonlocal model for plug formation in plates

By means of a nonlocal viscous fluid model, an investigation is carried out of the problem of penetration of a cylindrical projectile into a plate leading to a failure of the plate by a plug formation. The effect of impact is represented by a uniform initial velocity distribution over a circular region on the surface of the plate. The behavior of this plate material is assumed to be viscous and spatially nonlocal, and only the effects of vertical shearing stress are considered. The expression of stress, velocity and displacement are obtained and the calculated displacement profiles are compared with some existing experimental profiles.