High-temperature deformation behaviors of W/Zr based amorphous interpenetrating composite

The high-temperature tensile deformation behaviors of porous tungsten/zirconium-base metallic glass interpenetrating composites were examined systematically spanning a wide range of temperature. The deformations of composite at around supercooled liquid region all presented similar characteristics, including initial linear elastic behavior, obvious stress overshoot followed clear “work hardening”, which is different from that of monolithic BMG at high temperature close to the initial crystallization. The sample after tensile test still exhibited excellent compressive properties. The deformation and strengthening mechanisms were discussed in details. The W substrate dominates the deformation processes of the composite. The amorphous phase is helpful to the deformation and formability of the composite due to its good plastic deformation under high temperature. The results promise that the interpenetrating composite can be employed to produce parts using high-temperature forming techniques.     

Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load

This paper established a macroscopic constitutive model to describe the nonlinear stress–strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress–strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress–strain curves predicted by this model showed reasonable agreement with experimental results.     

Finite Element Analysis and Experimental Measurement of Deformation Behavior for NiTi Plate With Stress Concentration Part Under Uniaxial Tensile Loading

Abstract: The aim of this study is to verify the effectiveness of ordinary phenomenological constitutive relation of NiTi shape memory alloy under mechanical loading at a constant temperature, sufficiently. First, finite element analysis is performed by using ordinary phenomenological constitutive relation for rectangular plate with double notch under tensile loading at a constant temperature. Next, uniaxial tensile loading is carried out for 50.5Ni49.5Ti rectangular plate with double notch. At the same time, macroscopic stress–strain curve and local strain distribution are measured by using in‐house measurement system on the basis of digital image correlation. As a result, it is found that the stress–strain curve obtained from finite element analysis is much different from those obtained experimental measurement, especially during stress‐induced martensite transformation. The result can be derived from the phenomena of local strain band behavior arising in NiTi under mechanical loading. The phenomenological constitutive model used in present finite element analysis is constructed under assumptions that the material has isotropic characteristics and shows homogeneous deformation. However, this experimental result suggests that the material itself has anisotropy microscopically. Furthermore, material shows unique inhomogeneous deformation. Also, there is possibility that these anisotropic characteristic and inhomogeneous deformation behaviour may derive from its microstructure. In future, to sufficiently describe the macroscopic stress–strain curve of NiTi we should take into consideration the material microstructure.     

Influence of material nonlinearity on thermal distortion of polymer matrix composite panels

This paper discusses the influence of material nonlinearity on thermal distortion of polymer matrix composite panels. The load is transverse temperature gradient introduced by one-sided heat exposure, e.g., fire. For such low thermal conductivity materials, when there are no external mechanical loads, the transverse thermal gradient induces non-uniform thermal expansion along the thickness that results in transverse deformation field, known as thermal distortion. The power form stress–strain relation and the Ramberg–Osgood form stress–strain relation are discussed to include the temperature dependent behavior of polymer matrix composites. The degradation of polymer matrix composites at elevated temperature, thermal softening, is discussed. The variations of the reference stress and the reference strain with temperature are specified to describe the temperature dependent constitutive relationships. Semi-analytical simulation and finite element simulation are carried out for panels with roller end support condition. Results suggest that, while the material nonlinearity has insignificant influence on the transverse displacement of the panel, it has strong influence on local stress and strain. The stress and strain can go beyond the yield stress and the yield strain into plastic stage in certain circumstances.     

A constitutive model of particulate-reinforced composites taking account of particle size effects and damage evolution

This paper deals with a constitutive model of particulate-reinforced composites which can describe the evolution of debonding damage, matrix plasticity and particle size effects on deformation and damage. An incremental damage model of particulate-reinforced composites based on the Mori–Tanaka’s mean field concept has been extended to consider the particle size effects by using the Nan–Clarke’s simple method. The particle size effect on deformation is realized by introducing dislocation plasticity for stress–strain relation of in situ matrix in composites, and the particle size effect on damage is described by a critical energy criterion for particle–matrix interfacial debonding. For composites containing particles of various sizes, the effects of particle size distribution is incorporated into the model. Influence of debonding damage, particle size and particle volume fraction on overall stress–strain response of composites is discussed based on numerical results.     

Transverse compression behavior of Kevlar KM2 single fiber

This paper investigates the quasi static transverse compression behavior of Kevlar KM2 single fiber widely used in high velocity impact (HVI) applications. The nominal stress–strain response of single fibers exhibits nonlinear inelastic behavior under transverse compression. The nonlinearity is due to both geometric and material nonlinearities. The inelastic behavior is attributed to plastic deformation and microstructural damage resulting from fibrillation and micro cracking. The experimental set up allows for the observation and measurement of compressed width in real time. An experimental methodology is presented to determine the fiber material constitutive behavior by removing the geometric nonlinearity due to the growing contact area. Results from finite element model of the test method are correlated with the experimental results to assess the accuracy of the constitutive model.     

Temperature and strain rate dependence of deformation behavior of Zr65Al7.5Ni10Cu17.5

In this work, the effects of temperature and strain rate on the deformation behavior of Zr₆₅Al_7.5Ni₁₀Cu_17.5 bulk metallic glass (BMG) were investigated. It was found that both temperature and strain rate had a significant influence on the deformation behavior of the BMG. The alloy exhibited Newtonian behavior at low strain rates but showed non-Newtonian behavior at high strain rates in the supercooled liquid region. However, the crystallization occurred slightly at a strain rate of 2 × 10^?4 s^?1 at the temperature of 693 K that is lower than the crystallization temperature Tx of Zr₆₅Al_7.5Ni₁₀Cu_17.5 BMG. The deformation mechanisms were discussed in terms of the transition state theory based on the free volume model.     

A constitutive model for finite deformation response of layered polyurethane-montmorillonite nanocomposites

A constitutive model is developed to predict the finite deformation response of multilayered polyurethane (PU)-montmorillonite (MTM) nanocomposites. In PU-MTM nanocomposites, the PU matrix in the vicinity of the MTM nanoparticles is modified leading to an interphase region, and its effect on the finite deformation response of these nanocomposites is largely neglected in many existing models. In this work, the entire spatial volume is considered to be occupied by multi-layers of bulk PU and effective particles which consist of MTM nanoparticles and the modified PU interphase region. A Langevin chain based eight chain model is used to capture the large stretch hyperelastic behavior of bulk PU. The effective particle component of the model consists of a linear elastic spring to capture the initial elastic response, a non-linear viscoplastic dash-pot for the strain-rate dependent yield strength of nanocomposites, and a non-linear spring element in parallel to the dash-pot for the strain-hardening response. The model adopts the concept of amplified strain of the confined PU chains to accommodate the applied strain owing to the limited strain in the MTM nanoparticles. The constitutive model predicts all the major features of the stress-strain constitutive response of a family of PU-MTM nanocomposites including the initial linear elastic response, yield strength and post yield strain hardening for all volume fractions of MTM nanoparticles, thus confirming the efficacy of the proposed constitutive model.     

Constitutive modeling of woven composites considering asymmetric/anisotropic, rate dependent, and nonlinear behavior

The mechanical performance of woven composites was analyzed focusing on their nonlinear and rate dependent asymmetric/anisotropic deformation behavior. Three key characteristics were identified which are indispensable for realistically simulating the mechanical performance of woven composites: the asymmetric material behavior between tension and compression, its anisotropic and nonlinear evolution and rate dependency. To include all three characteristics into the nonlinear finite element analysis for woven composites, a phenomenological constitutive equation was developed based on an elasto-viscoplastic theory using the modified Drucker–Prager yield criterion and, in particular, developing the anisotropic nonlinear hardening law. A characterization method using both uniaxial tensile and compressive tests at different strain rates was proposed to determine the material properties for the constitutive equation. Then, the developed constitutive equation was incorporated into a finite element code and was validated by comparing the finite element simulation of the three points bending test with experiments.     

Constitutive equation and model validation for a 31 vol.% B4Cp/6061Al composite during hot compression

An accurate constitutive equation is essential to understanding the flow behavior of B₄C/Al composites during the hot deformation. However, the constitutive equations developed previously in literature are generally for low strain rate deformation. In the present work, we modified the general constitutive equation and take the high strain rate correction into account. The constitutive equation for a 31 vol.% B₄Cp/6061Al composite was constructed based on the flow stresses measured during isothermal hot compression at temperatures ranging from 375 to 525 °C and strain rates from 0.01 to 10 s^?1. The experimental flow stresses were corrected by considering temperature-dependent Arrhenius factor. The modified equation was then verified by using DEFORM-3D finite element analysis to simulate the experimental hot compression process. The results show that the modified equation successfully predicts flow stress, load–displacement, and the temperature rise. This helps to optimize the hot deformation process, and to obtain desirable properties, such as reduced porosity and homogenous particle distribution in B₄C/Al composites.     

Zr35Ti30Cu8.25Be26.75非晶合金在高速率下的高温流变本构模型

为研究锆基非晶合金在过冷液相区内较高温度区间和较高应变速率变形条件下的流变行为,准确描述温度和应变速率对非晶合金流变应力的影响,用Zwick/Roell力学性能实验机对Zr₃₅Ti₃₀Cu_8.25Be_26.75非晶合金进行高温(～1.2T_g)较高速(～10⁰/s)下的压缩实验,分别采用虚应力模型和提出的Maxwell-Pulse本构模型进行了应力、应变关系的表征。结果表明:Zr₃₅Ti₃₀Cu_8.25Be_26.75非晶合金的流变行为具有较强的温度和应变速率敏感性,即随着温度的降低和应变速率的升高,非晶合金的流变应力单调增加,同时其变形行为由平衡态牛顿流变转变为非平衡态的非牛顿流变;对比实验数据和模型预测数据发现,虚应力模型拟合结果偏差较大,误差大于50%,而Maxwell-Pulse本构模型预测值与实验值一致性好,准确率在90%以上,说明Maxwell-Pulse本构模型不仅能够同时描述Zr₃₅Ti₃₀Cu_8.25Be_26.75非晶合金的牛顿流变和非牛顿流变现象,也能够准确地反映Zr₃₅Ti₃₀Cu_8.25Be_26.75非晶合金在高温和较高应变速率变形条件下的应力应变关系。     

A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation

 This paper presents a rate-independent elastoplastic constitutive model for (nearly) incompressible biological fiber-reinforced composite materials. The constitutive framework, based on multisurface plasticity, is suitable for describing the mechanical behavior of biological fiber-reinforced composites in finite elastic and plastic strain domains. A key point of the constitutive model is the use of slip systems, which determine the strongly anisotropic elastic and plastic behavior of biological fiber-reinforced composites. The multiplicative decomposition of the deformation gradient into elastic and plastic parts allows the introduction of an anisotropic Helmholtz free-energy function for determining the anisotropic response. We use the unconditionally stable backward-Euler method to integrate the flow rule and employ the commonly used elastic predictor/plastic corrector concept to update the plastic variables. This choice is expressed as an Eulerian vector update the Newton's type, which leads to a numerically stable and efficient material model. By means of a representative numerical simulations the performance of the proposed constitutive framework is investigated in detail. Received: 12 December 2001 / Accepted: 14 June 2002 Financial support for this research was provided by the Austrian Science Foundation under START-Award Y74-TEC. This support is gratefully acknowledged.     

A finite element study of thermal relaxation of residual stress in laser shock peened IN718 superalloy

The residual stresses in laser shock peened (LSP) Inconel 718 Ni-base superalloy and their thermal relaxation behavior were investigated based on three-dimensional nonlinear finite element analysis. To account for the nonlinear constitutive behavior, the Johnson-Cook model has been employed and the model parameters for high strain rate response of IN718 are calibrated by comparison with recent experimental results. Based on the LSP simulation, the thermal relaxation behavior was studied through coupled thermal-structure analysis in LS-DYNA. More specifically, the effects of test temperature, exposure time and degree of initial plastic deformation are analyzed and discussed. It is observed that stress relaxation mainly occurs during the initial period of exposure, and the relaxation amplitude increases with the increase of applied temperature and as-peened plastic deformation. Based on the simulation results, an analytical model based on Zener-Wert-Avrami function is proposed to model the thermal residual stress relaxation.     

A method for measurement of multiple constitutive properties for composite materials

Accurate stress–strain constitutive properties are essential for understanding the complex deformation and failure mechanisms for materials with highly anisotropic mechanical properties. Among such materials, glass-fiber- and carbon-fiber-reinforced polymer–matrix composites play a critical role in advanced structural designs. The large number of different methods and specimen types currently required to generate three-dimensional allowables for structural design slows down the material characterization. Also, some of the material constitutive properties are never measured due to the prohibitive cost of the specimens needed. This work shows that simple short-beam shear (SBS) specimens are well-suited for measurement of multiple constitutive properties for composite materials and that can enable a major shift toward accurate material characterization. The material characterization is based on the digital image correlation (DIC) full-field deformation measurement. Two key elements show advantage of using DIC in the SBS tests. First, tensile, compressive, and shear stress–strain relations are measured in a single experiment. Second, a counter-intuitive feasibility of closed-form stress and modulus models, normally applicable to long beams, is demonstrated for short-beam specimens. The modulus and stress–strain data are presented for glass/epoxy and carbon/epoxy material systems.     

Microstructural modeling and simulation for GCr15 steel during elevated temperature deformation

The microstructural evolution of GCr15 steel, one of the most commonly used bearing steels, was investigated and simulated by physical experiments and finite element method (FEM). Physical experiments were conducted on the Gleeble-3500 thermo-simulation system. Effects of initial grain size and plastic strain on the microstructural of the materials were investigated by setting different heating temperature, holding time and deformation degree, respectively. Based on the results of stress–strain curves and metallographic analysis, the constitutive equations for flow stress, austenite grain growth and dynamic recrystallization of GCr15 steel were formulated by linear regression method and genetic algorithm. In addition, the coupled thermo-mechanical finite element method integrated with the developed constitutive models was used to simulate the microstructural evolution of GCr15 steel during hot compression. Good agreement between the calculated and experimental results was obtained, which confirmed that the developed constitutive models can be successfully used to predict microstructural evolution during hot deformation process for GCr15 steel.     

Rheological Behavior,Optimized Processing Interval,and Microreplication of a Zr‐Based Bulk Metallic Glass

Bulk metallic glass (BMG) is a novel advanced material developed since 1980s. In this paper, the Zr₃₅Ti₃₀Be_27.5Cu_7.5 BMG is prepared and its thermoplastic forming (TPF) tests at various strain rate with different temperatures in supercooled liquid region (SCLR) are conducted. According to differential scanning calorimetry (DSC) curve and the transformed Kissinger equation, the normally processable temperature window (588–731 K) and continuous heating transformation (CHT) curve are obtained, respectively. And the isothermal annealing experiments without deformation are performed at 663, 683, 703, and 713 K with various holding times, respectively, results of which obviously suggest that the deformation during TPF can induce crystallization. Notably, from CHT curve and TPF tests, the optimized processing interval is subsequently revealed. All evidence indicates that this alloy presents good superplastic‐like behavior with a relatively low level of flow stress and large plastic strain under the temperature ranging from 643 to 703 K and the strain rate of 1 × 10^?2 s^?1–5 × 10^?4 s^?1. Furthermore, the successful microreplication and molding of several coins and microparts under the condition of strain rate of an order of 10^?3 s^?1 at 663 K also provides us with the full proof for extremely good thermoplastic formability in this alloy.

     

Damage-induced stress-softening and viscoelasticity of limited elastic materials

The rate-dependent behavior of filled natural rubber (NR) is investigated in tensile regime. In order to describe the viscosity-induced rate-dependent effects, a constitutive model of finite strain viscoelasticity is proposed on the basis of the multiplicative decomposition of the deformation gradient tensor into elastic and viscous parts. The total stress is decomposed into an equilibrium stress and a viscosity-induced overstress by following the rheological models of Poynting–Thomson and Zener types. To incorporate the Mullins stress-softening phenomenon into a viscoelastic material, an invariant-based stress-softening function is also proposed. To identify the constitutive equation for the viscosity from direct experimental observations, an analytical scheme is proposed that ascertains the fundamental relation between the viscous strain rate and the overstress tensor with limited elastic parent material model. Evaluation of the experimental results using the proposed analytical scheme confirms the necessity of considering both the current overstress and the current deformation as variables to describe the evolution of the rate-dependent phenomena. Based on this, an evolution equation is proposed to represent the effects of internal variables on viscosity phenomena. The proposed evolution equation has been incorporated into the finite-strain viscoelasticity model in a thermodynamically consistent way.