Development of viscoelastic/rate-sensitive-plastic constitutive law for fiber-reinforced composites and its applications Part II: Numerical formulation and verification

The viscoelastic/rate-sensitive plastic constitutive law to describe the non-linear, anisotropic/asymmetric and time/rate-dependent mechanical behavior of fiber-reinforced (sheet) composites were developed as discussed in Part I along with experimental procedures to obtain the material parameters for the woven fabric composite. Here, numerical formulations were developed. For verification purposes, finite element simulation results based on the proposed constitutive law were compared with experiments for the time-dependent springback in rate-dependent three point bending tests.     

Development of viscoelastic/rate-sensitive-plastic constitutive law for fiber-reinforced composites and its applications. Part I: Theory and material characterization

The viscoelastic/rate-sensitive plastic constitutive law to describe the nonlinear, anisotropic/asymmetric and time/rate-dependent mechanical behavior of fiber-reinforced (sheet) composites was developed under the plane stress condition. In addition to the theoretical aspect of the developed constitutive law, experiments to obtain the material parameters were also carried out for the woven fabric composite based on uni-axial tension and compression tests as well as stress relaxation tests, while the numerical formulation and verifications with experiments are discussed in Part II.     

Anisotropic creep modeling of coated textile membrane using finite element analysis

Coated textile membranes (CTMs) form a class of flexible textile composites undergoing viscoelastic deformation because they consist of a polymeric reinforcement and matrix and are tensioned in service. In most CTMs, woven fabrics are frequently used as a reinforcement structure, causing anisotropic mechanical behavior including time dependent viscoelastic deformation. To describe such anisotropic and nonlinear time dependent deformation, the creep potential with three orthotropic parameters was introduced and incorporated into finite element software through a user material subroutine. The three parameters included in the creep potential were determined by carrying out off-axis coupon creep tests and using various mathematical formulae for the effective creep compliance. To validate the current creep modeling and its implementation in finite element software, off-axis coupon creep tests were re-simulated and compared with the experiments, showing that the present modeling can describe the anisotropic and nonlinear creep deformation of CTM with acceptable accuracy.     

考虑拉剪耦合的二维编织物各向异性超弹性本构模型

基于连续介质力学理论,提出了一种考虑二维编织物拉剪耦合作用的各向异性超弹性本构模型。该模型中应变能被分解为纤维拉伸应变能和拉剪耦合作用下的剪切应变能两部分。给出了模型参数的确定方法,通过拟合实验数据,得到了本构模型参数。利用确定的本构模型对文献中不同预拉状态下的镜框剪切实验进行了预测,通过与实验结果对照,验证了所提出的本构模型正确性。该模型不仅具有明确的物理意义且参数确定简单,为更加全面精确的二维编织物成型有限元分析奠定了理论基础。     

Finite element simulation and experimental study on mechanical behavior of 3D woven glass fiber composite sandwich panels

The results of finite element simulation followed by an experimental study are presented in order to investigate the mechanical behavior of three-dimensional woven glass-fiber sandwich composites using FE method. Experimental load–displacement curves were obtained for flatwise compressive, edgewise compressive, shear, three-point bending and four-point bending loads on the specimens with three different core thicknesses in two principal directions of the sandwich panels, called warp and weft. A 3D finite element model is employed consisting of glass fabric and surrounding epoxy resin matrix in order to predict the mechanical behavior of such complex structures. Comparison between the finite element predictions and experimental data showed good agreement which implies that the FE simulation can be used instead of time-consuming experimental procedures to study the effect of different parameters on mechanical properties of the 3D woven sandwich composites.     

Sheet hydroforming of woven FRT composites: non-orthogonal constitutive equation considering shear stiffness and undulation of woven structure

For the simulation of sheet hydroforming for the shaping of woven fabric reinforced thermo-plastic (FRT) composites, a non-orthogonal constitutive model was developed based on a homogenization method by considering the microstructures of composites including mechanical and structural properties of the fabric reinforcement. This model is modified to capture the wrinkling behavior due to the undulation geometry of the woven structure and shear stiffness at the crossover of the warp and weft yarns of woven FRT composites. The model was implemented in an explicit dynamic finite element code to analyze the forming behavior of woven FRT during the stamp thermo-hydroforming process. Wrinkling behavior was investigated based on the application of a counteracting fluid pressure and changes to the initial blank shape.     

A stochastic plasticity approach to strength modeling of strand-based wood composites

A 3 dimensional stochastic finite element technique is presented herein for simulating the nonlinear behaviour of strand-based wood composites with strands of varying grain-angle. The approach is based on the constitutive properties of the individual strands to study the effects of varying strand characteristics (such as species or geometry) on the performance of the member. The constitutive properties of the strands are found empirically and are subsequently used in a 3 dimensional finite element program. The program is formulated in a probabilistic manner using random variable material properties as input. The constitutive model incorporates classic plasticity theory whereby anisotropic hardening and eventual failure of the material is established by the Tsai–Wu criterion with an associated flow rule. Failure is marked by an upper bound surface whereupon either perfect plasticity (i.e. ductile behavior) or an abrupt loss of strength and stiffness (i.e. brittle behavior) ensues. The ability of this technique to reproduce experimental findings for the stress–strain curves of angle-ply laminates in tension, compression as well as 3 point bending is validated.     

A constitutive model for self-reinforced ductile polymer composites

Self-reinforced polymer composites are gaining increasing interest due to their higher ductility compared to traditional glass and carbon fibre composites. Here we consider a class of PET composites comprising woven PET fibres in a PET matrix. While there is a significant literature on the development of these materials and their mechanical properties, little progress has been reported on constitutive models for these composites. Here we report the development of an anisotropic visco-plastic constitutive model for PET composites that captures the measured anisotropy, tension/compression asymmetry and ductility. This model is implemented in a commercial finite element package and shown to capture the measured response of PET composite plates and beams in different orientations to a high degree of accuracy.     

三维正交机织玻璃纤维/环氧树脂复合材料动态力学性能的实验和理论研究

通过实验系统研究了三维正交机织玻璃纤维/环氧树脂复合材料厚度方向和面内方向的动、 静态压缩力学性能。结果表明, 动、 静态压缩载荷作用下该材料响应表现出明显的各向异性、 非线性和应变率敏感性。针对三维正交机织玻璃纤维/环氧树脂复合材料高速变形过程中不同形式的内部缺陷和微损伤的演化, 提出了一个依赖应变、 应变率的宏观损伤量, 建立了一种含损伤的非线性黏弹性本构模型。采用数据处理方法拟合了其本构方程材料参数, 在加载过程中, 模型计算值与实验结果吻合较好。     

Multiscale progressive failure analysis of textile composites

The experimental determination of stiffness and strength of textile composites is expensive and time-consuming. Experimental tests are only capable of delivering properties of a whole textile layer, because a decomposition is not possible. However, a textile layer, consisting of several fiber directions, has the drawback that it is likely to exhibit anisotropic material behavior. In the presented paper a finite element multiscale analysis is proposed that is able to predict material behavior of textile composites via virtual tests, solely from the (nonlinear) material behavior of epoxy resin and glass fibers, as well as the textile fiber architecture. With these virtual tests it is possible to make predictions for a single layer within a textile preform or for multiple textile layers at once. The nonlinear and pressure-dependent behavior of the materials covered in the multiscale analysis is modeled with novel material models developed for this purpose. In order to avoid mesh-dependent solutions in the finite-element simulations, regularization techniques are applied. The simulations are compared to experimental test results.     

考虑双拉耦合的复合材料编织物各向异性超弹性本构模型

为了准确描述复合材料编织物的各向异性力学特性,首先,基于纤维增强复合材料连续介质力学理论提出了一种考虑纤维双拉耦合的复合材料编织物各向异性超弹性本构模型,该模型中单位体积的应变能被解耦为便于参数识别的纤维拉伸变形能、双拉耦合引起的挤压变形能和纤维间角度变化产生的剪切变形能;然后,给出了模型参数的确定方法,并通过拟合单轴拉伸、双轴拉伸和镜框剪切实验数据得到了本构模型参数;最后,利用该模型对双轴拉伸和镜框剪切实验进行了数值仿真,并将模拟结果与实验结果对比分析。结果表明:提出的本构模型适用于表征复合材料编织物在成型过程中由于大变形引起的非线性各向异性力学行为。所得结论表明提出的本构模型具有简单、实用的优点,且材料参数容易确定,可为复合材料编织物成型的数值模拟和工艺优化奠定理论基础。      

Mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air voids

In random-chopped fiber-reinforced polymer (FRP) composites used as a retrofit material, a high volume fraction of voids is inevitable due to the manufacturing characteristics. In this paper, the mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air porosity are investigated through experiments and numerical analysis. Coupon-shaped specimens with various material compositions were manufactured to examine the uniaxial tensile performance, and the air voids in the composites were measured by a microscope camera. In order to predict the overall performance of the composites, a micromechanical formulation that accounts for porosity was newly developed. The derived model was incorporated into a finite element (FE) code, and the model parameters were estimated by comparing uniaxial tensile test results for various systems of random-chopped FRP composites. In addition, concrete beams strengthened with the composites were produced to evaluate their load-carrying capacity. The FE predictions of the composite structures were then compared with experimental data to verify the predictive capability of the proposed numerical framework.     

Multiscale finite element modeling of failure process of composite laminates

A multiscale nonlinear finite element modeling technique is developed in this paper to predict the progressive failure process for composite laminates. A micromechanical elastic–plastic bridging constitutive model, which considers the nonlinear material properties of the constituent fiber and matrix materials and their interaction and the damage and failure in fibrous composites at the fiber and matrix level, is proposed to represent the material behavior of fiber-reinforced composite laminates. The micromechanics constitutive model is employed in the macroscale finite element analysis of structural behavior especially progressive failure process of the fiber-reinforced composites based on a 4-node 24-DOF shear-locking free rectangular composite plate element.     

Finite Element Analysis of 2.5D Woven Composites,Part II: Damage Behavior Simulation and Strength Prediction

In the first part of the work, a new 2.5D woven composites finite element model (2.5D WCFEM) which took into consideration the impact of face structures and can accurately predict the main elastic performances has been established. In this part, the stress–strain behavior and the damage characteristic of this material under uniaxial tension are simulated using nonlinear progressive damage analysis based on damage mechanics. Meanwhile, experimental investigation and fracture analysis are conducted to evaluate the validity of the proposed method. Finally, the influence of woven parameters on the mechanical behavior is discussed. Compared with the test results, a good agreement between the computational and experimental results has been obtained. The progressive damage characteristic and main failure modes are also revealed.     

Numerical study on thermo-stamping of woven fabric composites based on double-dome stretch forming

Through the international corporative benchmark works, the material characterization of the woven fabric composites has been examined to better understand their mechanical properties and to provide the process design information for numerical analysis. As the second stage of the benchmark work, the double-dome geometry has been used to illustrate the effect of numerical schemes on the forming behaviors of the woven composites parts. To account for the change of fiber orientation under the large deformation, the non-orthogonal constitutive model was utilized and nonlinear friction behavior was incorporated in the simulation. The equivalent material properties based on the contact status were used for the thermo-stamping process. Furthermore, we incorporated a recently developed non-orthogonal model which captures the dependency of shear behavior of woven fabric composites on the tensions in yarns. Simulation results showed the effect of coupling on the predicted forming behavior for the double-dome parts. As numerical results, blank draw-in, punch force history and fiber orientation after forming have been compared based on various numerical models and methods.     

Magneto-Mechanical Finite Element Analysis of Single Crystalline Ni2MnGa Ferromagnetic Shape Memory Alloy

Based on an existing micromechanical constitutive model for Ni2MnGa ferromagnetic shape memory alloy single crystals, a three-dimensional quasi-static isothermal incremental constitutive model that is suitable for finite element analysis is derived by using Hamilton's variational principle. This equation sets up the coupling relation between the magnetic vector potential and the mechanical displacement. By using the incremental equation and ANSYS software, the mechanical behaviors of martensitic variant reorientation for Ni2MnGa single crystals are analyzed under magneto-mechanical coupling action. And the finite element results agree well with the experimental data. The methods used in the paper can well describe the mechanical behaviors of the material in complex fields.     

碳纤维织物力学性能和冲压成形实验研究

在实际成形过程中,碳纤维复合材料往往处于复杂的应力状态,开展近于真实载荷环境下的力学试验分析,能够更准确地认识实际应用中材料的成形性能和变形机理.为获得碳纤维织物的基本力学特性,设计了平纹碳纤维织物拉伸试样及成形试样,进行了单轴拉伸、双轴拉伸、镜框剪切试验和方盒冲压成形实验研究,对比了不同双拉比及纱线取向对力学性能及成形性能的影响.研究结果表明:碳纤维织物具有高度的非线性、各向异性和双拉耦合特性,即经纬向纤维的力学性能会相互影响;剪切变形是成形过程中的主要变形模式,当剪切角达到临界锁死角时,织物发生起皱现象;同种织物不同纱线取向试样表现出不同的成形性能,因此可以根据零件几何形状选择合适纤维取向的织物,从而减少缺陷,优化成形零件的力学性能.研究结果为后续建立碳纤维织物本构模型和成形仿真奠定了基础.     

Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.     

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.     

Progressive damage modeling for large deformation loading of composite structures

A nonlinear constitutive model for large deformation loading at different strain rate condition was developed to represent tensile progressive damage of the nonlinear large deformation rate dependent behavior of polymer-based composite materials. The material was characterized by using off-axis composite specimens at different strain rates. A new failure criterion was proposed for the analysis of different loading directions and strain rates. Based on a method of combining the nonlinear constitutive theory and the proposed failure criterion for different strain rates, the progressive damage behavior of large deformation composites was represented. The strength of the material was also successfully represented with a single material constant.