Investigations to the effect of heating-rate on the mechanical properties of aluminum alloy LY12

Two classes of experiments were conducted with a Gleeble 1500 thermal–mechanical testing system to investigate the effect of heating-rate and its history on the mechanical behavior of aluminum alloy LY12. In the first class of experiment, specimens were heated at different heating-rates to prescribed temperatures and then stretched until fracture. It was found that the specimen heated with higher heating-rate possesses lower rupture strength. In the second class of experiment, the specimens were preloaded and then heated at different rates until fracture. It was found that the higher the heating-rate was, the lower the failure temperature would be. Metallographical analysis showed that there are more defects in the specimens undergoing higher heating-rate. It was conjectured that higher heating-rate may cause stronger local thermal inconsistency due to the heterogeneous nature of the material. It may then cause local residual microstress fields, which, together with external thermal–mechanical load, may result in the changes in the microstructure of the material, such as recovery, recrystallization, nucleation and growth of microdefects, accounting for the changes in the macroscopic mechanical properties including hardening/softening, damage and failure, etc. A numerical simulation was performed, in which the mechanisms of local thermal inconsistency and the effect of the influencing factors were investigated.     

高周疲劳的损伤-硬化模型

两级循环加载条件下,材料的剩余寿命强烈地依赖于加载历史。究其原因,不同加载历史将引起材料的微结构发生不同的变化,使得材料的硬化效果和变形行为表现出明显的差异,从而影响了损伤的演化过程。本文引入硬化状态变量来表征加载历史对疲劳损伤演化过程的影响。通过对两级循环加载下损伤演化规律和剩余寿命的研究,认为在两级（或多级）加载条件下,材料的损伤演化和剩余寿命强烈地依赖于加载历史造成的损伤和硬 化状态。     

An examination of the competition between bulk behavior and interfacial behavior of ceramics subjected to dynamic pressure-shear loading

A grain level micromechanical analysis of ceramic microstructures subjected to dynamic compression-shear loading conditions is presented. The investigation consists of a combined experimental/numerical approach in which bulk and surface properties are examined by means of pressure-shear impact experiments for a ceramic plate in contact with steel plates. The model for the ceramic microstructure accounts for heterogeneities and randomness in grain orientation and composition. A cohesive zone model is included to capture inter-granular microcrack initiation and evolution as a natural outcome of the calculated material response. Surface roughness is also included in the analysis to capture the time-dependent frictional behavior of the various interfaces. The model for the steel anvil plate accounts for visco-plasticity, thermal softening and strain hardening. Representative volume elements of ceramic microstructure and anvil plates are considered to account for features observed in real experiments. Pressure-shear impact velocity histories are used not only to identify inelasticity, but also to determine dominant failure modes. Bridging between micro- and macroscales is achieved by using the developed model. Simulated velocity histories have been found to be in a good agreement with the experimental observations when bulk and surface features are included in the analysis. However, it is demonstrated that information gathered from these experiments is not sufficient to determine the mechanical behavior of the brittle material. Instead, the velocity histories provide important information on the time-dependent frictional behavior of the specimen-anvil interfaces.     

Comparison of isotropic hardening and kinematic hardening in thermoplasticity

A coupled thermo-mechanical problem is presented in this paper. The constitutive model is based on thermoplastic model for large strains where both kinematic and isotropic hardening are included. It is shown that a non-associated plasticity formulation enables thermodynamic consistent heat generation to be modeled, which can be fitted accurately to experimental data. In the numerical examples the effect of heat generation is investigated and both thermal softening and temperature-dependent thermal material parameters are considered. The constitutive model is formulated such that pure isotropic and pure kinematic hardening yield identical uniaxial mechanical response and mechanical dissipation. Thus, differences in response due to hardening during non-proportional loading can be studied. Thermally triggered necking is studied, as well as cyclic loading of Cook’s membrane. The numerical examples are solved using the finite element method, and the coupled problem that arises is solved using a staggered method where an isothermal split is adopted.     

Cyclic behavior of unidirectional and cross-ply titanium matrix composites

Relatively simple and efficient micromechanical models are used to obtain the uniaxial response of SCS-6/Timetal 21S with [0]₄ and [0/90]_s laminates when subjected to isothermal and thermomechanical fatigue (TMF) loadings. Features of the modeling that are required to obtain the accurate deformation behavior for this class of materials under these loadings are highlighted. To this end, a comparison is made between the concentric cylinder model and the uniaxial stress model for representing the [0] laminate. The axial stresses from the two models are very similar under mechanical loading. The greatest differences appear under thermal loading alone. The differences on the composite response between a time-independent elastic-plastic and a viscoplastic matrix constitutive model are also examined. The latter is based on the Bodner-Partom unified constitutive model. The [0/90] laminate is treated by adding a parallel element with smeared [90] ply properties to the [0] model and invoking axial strain compatibility as well as stress equilibrium. The proposed constitutive law for the [90] ply includes both matrix viscoplasticity and fiber/matrix separation damage and is based on damage mechanics concepts. The effect of cyclic frequency on TMF behavior is examined. The in-phase TMF life is shown to be very sensitive to frequency due to the relaxation of matrix stress and the attendant increase in fiber stress.     

304不锈钢室温和高温单轴循环塑性的实验研究

对304不锈钢进行了室温和高温单轴应变控制和应力控制下的系统循环试验。揭示和分析了循环应变幅值、平均应变及其历史和温度历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史以及温度对循环棘轮行为的影响。也讨论了应变循环和应力循环间交互作用对材料循环塑性行为的影响。研究表明,无益单轴应变循环特性还是非对称单轴应力循环下的棘轮效应不仅取决于当前温度和加载状态,而且强烈依赖于其加载历史。研究得到了一些有助于304不锈钢室温和高温单轴循环行为本构描述的结果。     

基于石膏材料的小结构重力坝损伤本构模型研究

大坝模型试验的模型材料力学性能是试验成功与否的关键影响因素。基于石膏模型材料基本力学性质和混凝土材料基本相似的实际情况,考虑石膏模型材料的孔隙率,在能量损伤理论模型的基础上,结合工程规范,建立了石膏模型材料的受拉损伤本构模型。同时,分析了模型材料应变率对材料峰值应力的影响,引入动应力提高系数,并给出了与应变率相关的模型材料受拉损伤本构模型。利用该本构模型模拟了动荷载下石膏模型重力坝的破坏过程,并与模型试验结果进行对比。结果表明：数值模拟得到的重力坝开裂破坏的位置、形式与模型试验结果较为接近。     

Biothermomechanics of skin tissues

Biothermomechanics of skin is highly interdisciplinary involving bioheat transfer, burn damage, biomechanics and neurophysiology. During heating, thermally induced mechanical stress arises due to the thermal denaturation of collagen, resulting in macroscale shrinkage. Thus, the strain, stress, temperature and thermal pain/damage are highly correlated; in other words, the problem is fully coupled. The aim of this study is to develop a computational approach to examine the heat transfer process and the heat-induced mechanical response, so that the differences among the clinically applied heating modalities can be quantified. Exact solutions for temperature, thermal damage and thermal stress for a single-layer skin model were first derived for different boundary conditions. For multilayer models, numerical simulations using the finite difference method (FDM) and finite element method (FEM) were used to analyze the temperature, burn damage and thermal stress distributions in the skin tissue. The results showed that the thermomechanical behavior of skin tissue is very complex: blood perfusion has little effect on thermal damage but large influence on skin temperature distribution, which, in turn, influences significantly the resulting thermal stress field; the stratum corneum layer, although very thin, has a large effect on the thermomechanical behavior of skin, suggesting that it should be properly accounted for in the modeling of skin thermal stresses; the stress caused by non-uniform temperature distribution in the skin may also contribute to the thermal pain sensation.     

长期中子辐照 Al-Mg-Si合金的压缩力学行为

利用材料试验机及分离式霍普金森压杆装置,开展长期中子辐照后的Al-Mg-Si合金（反应堆内实际服役近30年的LT21铝合金）在不同温度和应变率下压缩力学行为的实验研究,获得了实验温度、应变率对其屈服强度及流动应力的影响规律。结果表明:材料在一定的温度区间（?40～300 ℃）和应变率区间（0.001～3 000 s?1）内,分别呈现出较为明显的温度效应与正应变率效应;其中在较低的温度（?80～?40 ℃）和较高的应变率（3 000～5 000 s?1）区间力学性能受温度和应变率变化的影响较小;当温度升至300 ℃时,材料的塑性变形行为已趋于理想塑性流动。根据前述实验结果,计及材料内部的微观辐照缺陷对力学性能的影响,建立了考虑辐照损伤的Zerilli-Armstrong本构模型,模型的计算结果与前述实验结果吻合较好。结合文献中高纯铝的微观辐照缺陷的演化数据,对不同快中子辐照剂量LT21铝合金的屈服强度,以及另两个来自反应堆内不同受辐照区域试样在不同应变率和温度下的屈服强度进行了计算。上述研究表明,本文建立的考虑辐照损伤的Z-A本构方程不仅能较好地反映长期中子辐照后的Al-Mg-Si合金宏观应力和应变、应变率、温度等参数的关系,也能针对位错运动及辐照硬化机制进行较好地描述,并且能够为反应堆内相应结构元件的设计、运行和安全评估提供一定的参考。     

A three-dimensional model of anisotropic hardening in metals and its application to the analysis of sheet metal formability

The hardening model proposed by Z. Mróz based on the uniaxial fatigue behavior of many metals is adopted to derive an incremental constitutive equation for general three-dimensional problems. This constitutive law is then employed in the analysis of metal forming problems to assess the influence of loading cycles, of the types involved in standard forming processes, on the ultimate formability of sheet metals. The predicted forming limit curves differ quantitatively from results obtained via an isotropie hardening model and differ qualitatively from those obtained via a kinematic model. Also investigated are the effects of such loading cycles on material response to simple tensile loading, which is often used to characterize a material. Significant differences between the present model and the other two models considered are observed in such characterizers of simple tensile behavior as the stress-strain curve, the anisotropy parameter and the uniform elongation. These differences suggest a rather simple experiment to identify the proper material model to be used in analyses of problems which involve loading cycles. Comparisons with some experimental results reveal that the employment of an anisotropic hardening model, such as the generalized Mróz model derived herein, is indeed crucial in accurately predicting material response to complicated loading histories.     

Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations

The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.     

A thermodynamic consistent damage and healing model for self healing materials

Thermodynamics of the damage and the healing processes for viscoplastic materials is discussed in detail and constitutive equations for coupled inelastic-damage-healing processes are proposed in a thermodynamic consistent framework. Small deformation state is utilized and the kinematic and the isotropic hardening effects for the damage and healing processes are introduced into the governing equations. Two new yield surfaces for the damage and healing processes are proposed that take into account the isotropic hardening effect. The computational aspect for solving the coupled elasto-plastic-damage-healing problem is investigated, and the mechanical behavior of the proposed polymeric based self healing system is obtained. Uniaxial compression tests are implemented on a shape memory polymer based self healing system and the damage and the healing are captured by measurement of the changes in the modulus of elasticity. It is concluded that the proposed constitutive equations can model the damage and healing effectively and the mechanical behavior of a shape memory polymer based self healing system can be precisely modeled using this formulation.     

A viscoplastic constitutive model for nickel-base superalloy,part 2: modeling under anisothermal conditions

In Part 2 of this study, extensive deformation tests were carried out on the nickel-base polycrystalline superalloy IN738LC under isothermal and anisothermal conditions between 450 and 950 °C. Under the isothermal conditions, the material showed almost no rate/time-dependency below 700 °C, while it showed distinct rate/time-dependency above 800 °C. Regarding the cyclic deformation, slight cyclic hardening behavior was observed when the temperature was below 700 °C and the imposed strain rate was fast, whereas in the case of the temperature above 800 °C or under slower strain rate conditions, the cyclic hardening behavior was scarcely observed. Unique inelastic behavior was observed under in-phase and out-of-phase anisothermal conditions: with an increase in the number of cycles, the stress at higher temperatures became smaller and the stress at lower temperatures became larger in absolute value although the stress range was approximately constant during the cyclic loading. In other words, the mean stress continues to evolve cycle-by-cycle in the direction of the stress at lower temperatures. Based on the experimental results, it was assumed that evolution of the variable Y that had been incorporated into a kinematic hardening rule in Part 1 of this study is active under higher temperatures and is negligible under lower temperatures. The material constants used in the constitutive equations were determined with the isothermal data, and were expressed as functions of temperature empirically. The extended viscoplastic constitutive equations were applied to the anisothermal cyclic loading as well as the monotonic tension, stress relaxation, creep and cyclic loading under the isothermal conditions. It was demonstrated that the present viscoplastic constitutive model was successful in describing the inelastic behavior of the material adequately, including the anomalous inelastic behavior observed under the anisothermal conditions, owing to the consideration of the variable Y.     

Constitutive modeling of cyclic plasticity deformation of a pure polycrystalline copper

Cyclic plasticity experiments were conducted on a pure polycrystalline copper and the material was found to display significant cyclic hardening and nonproportional hardening. An effort was made to describe the cyclic plasticity behavior of the material. The model is based on the framework using a yield surface together with the Armstrong–Frederick type kinematic hardening rule. No isotropic hardening is considered and the yield stress is assumed to be a constant. The backstress is decomposed into additive parts with each part following the Armstrong–Frederick type hardening rule. A memory surface in the plastic strain space is used to account for the strain range effect. The Tanaka fourth order tensor is used to characterize nonproportional loading. A set of material parameters in the hardening rules are related to the strain memory surface size and they are used to capture the strain range effect and the dependence of cyclic hardening and nonproportional hardening on the loading magnitude. The constitutive model can describe well the transient behavior during cyclic hardening and nonproportional hardening of the polycrystalline copper. Modeling of long-term ratcheting deformation is a difficult task and further investigations are required.     

电磁加热条件下皮肤组织的生物热力学行为

研究目的是开发一种数学方法来计算传热过程、热引起的力学响应以及相应的疼痛等级, 从而对临床上应用的各种加热疗法之间的差别进行定量评估. 采用基于有限差分法的数值模拟方法, 基于无限大和均匀化假设, 分析了各种热疗法中皮肤组织的温度、烧伤和热应力分布. 研究发现: 充血对热损伤的影响很小, 但对皮肤的温度分布影响很大, 而这又反过来显著影响由此产生的热应力场; 对于激光加热, 光波越短则峰值温度越高, 但峰值更接近皮肤表面温度; 激光和微波加热所产生的热应力集中于表皮顶层, 因为发热量沿皮肤深度方向呈指数衰减; 薄角质层(常常被忽略)对皮肤组织的热力学响应起主导作用.      

弹体贯穿混凝土数值模拟的改进材料模型

研究混凝土结构在冲击载荷下的力学特性对武器以及防护结构的设计和评估具有重要意义,而合适的材料模型可以更准确地预测混凝土结构的力学行为和破坏模式。因此,本文中提出了一种改进的混凝土塑性损伤材料模型来描述其在冲击载荷下的力学响应。该改进模型考虑了压力-体积应变关系、应变率效应、洛德角效应和塑性损伤累积对混凝土材料力学特性的影响,并引入了一个与损伤相关的硬化/软化函数来描述压缩状态下的应变硬化和软化行为。随后,通过对3个独立的强度面进行线性插值得到了该改进模型的破坏强度面,并采用部分关联流动法则考虑了混凝土材料的体积膨胀特性。最后,开展了单个单元在不同加载条件下和弹体贯穿钢筋混凝土靶的数值模拟,验证了该改进模型的可行性、准确性以及预测性能提升。     

THERMOMECHANICAL RESPONSE OF SMA FIBER COMPOSITES WITH NON-UNIFORM TEMPERATURE DISTRIBUTION

A micromechanics method based on the High-Order-Theory developed by Aboudi et al. is used to predict the thermomechanical response of composites reinforced by shape memory alloy (SMA) fibers, and the non-uniform thermal distribution in composite arising from the process of heating or cooling is considered. The numerical development based on this model was coded to predict the thermomechanical response of shape memory alloy fiber/elastomer matrix composite subjected to thermal cycle loading. When the composite is heated, two heating ways, thermal gradients and heat source by passing an electric current through the SMA fibers are imposed on the composite respectively. Upon cooling, the first thermal boundary condition and the second thermal boundary condition are subjected to the composite respectively. A series of stress distributions and temperature distributions for different instants are calculated to reveal the interaction between the SMA material and matrix. It is useful to analyze and design the SMA actuator driven by heat source or the surface temperature.     

Micromechanical analysis of the fully coupled finite thermoelastic response of rubber-like matrix composites

A micromechanical analysis for the prediction of the coupled thermoelastic response of multiphase composites that include rubber-like phases is presented. Rubber-like solids are highly nonlinear thermoelastic materials that exhibit anomalous behavior referred to as the thermoelastic inversion effect. Results are presented which show that the derived micromechanical model is capable of predicting this effect in nylon/rubber composites subjected to appropriate thermal loadings assuming one-way coupling. For full thermomechanical coupling, the nonlinear response and induced temperatures under several types of mechanical loading are investigated.