A micromechanical compaction model for woven fabric preforms. Part II: Multilayer

With nesting between adjacent layers and inter-layer packing, the microstructure and the compaction behaviour of a multilayer woven fabric preform are much more complicated than those of a single layer fabric preform. A micromechanical model, based on the hierarchical structure characteristics of woven fabric preforms, was developed to investigate the elastic compaction behaviour of multilayer plain weave fabric preforms. The compaction mechanisms of fabrics at different hierarchical levels including deformation and compaction of yarn cross-section, flattening of yarn waveform, nesting between adjacent layers and inter-layer packing, are considered in an integrated approach in this predictive model. Effects of structural elements at different hierarchical levels on compaction behaviour of multilayer plain weave fabric preforms are investigated in detail. Both the number of layers and shifting are shown to have significant effects on compaction behavior, while the effect of nesting increases as the number of layers increases. The predictions by this model are correlated well with the experimental data.     

Three-dimensional computational micro-mechanical model for woven fabric composites

This work presents a computational material model for plain-woven fabric composite for use in finite element analysis. The material model utilizes the micro-mechanical approach and the homogenization technique. The micro-mechanical model consists of four sub-cells, however, because of the existing anti-symmetry only two sub-cells have to be homogenized for prediction of the elastic material properties. This makes the model computationally very efficient and suitable for large-scale finite element analysis. The model allows the warp and fill yarns not to be orthogonal in the plane of the composite ply. This gives the opportunity to model complex-shaped composite structures with different braid angles. General homogenization procedure is employed with two levels of property homogenization. The model is programmed in MATLAB software and the predicted material properties of different composite materials are compared and presented. The material model shows good capability to predict elastic material properties of composites and very good computational efficiency.     

An analytical model for perforation of ceramic/multi-layered planar woven fabric targets by blunt projectiles

An analytical model has been developed in this paper for perforation of ceramic/multi-layer woven fabric targets by blunt projectiles. In previous Chocron–Galvez analytical model the semi-angle of ceramic conoid is constant and the strain rate effects are also neglected in the stress–strain behavior of the yarns and only strain energy absorbed by the yarns is considered.     

A three-dimensional micromechanical model to predict the viscoelastic behavior of woven composites

Polymer matrix based cloth composites are increasingly used in engineering applications. For such composites, significant viscoelastic behavior can be observed for dynamic load conditions. The viscoelastic effect is primarily due to the polymeric matrix used as most of the fibers used in structural applications are elastic. Matrix does not show a major contribution in the axial properties of composites, thus in the traditional modeling its viscoelastic nature is often ignored. However, the effective out of plane properties are influenced by the matrix material and exhibit significant damping characteristics. Therefore, a complete three-dimensional (3-D) model considering the viscoelastic nature of matrix is needed for better understanding of cloth composites. An analytical 3-D micromechanical model based on classical laminate theory (CLT) is verified, in this paper for the prediction of effective elastic and viscoelastic properties of a cloth composite. The method is shown to be accurate. This model is extended to the viscoelastic regime with the use of Laplace transform and correspondence principle. Prony series coefficients for composite cloth are obtained for different volume fractions of fibers in yarn. It is observed from the hysteresis plots that dissipation in out of plane normal and shear modes is significantly higher than the normal directions.     

碳纤维机织物增强热塑性树脂复合材料热冲压叠层模型

针对碳纤维增强热塑性树脂复合材料(CFRTP)在热冲压成型过程中涉及到大变形、各向异性和多场耦合的现象,为了表征CFRTP在成型中的力学特征,基于有限元方法与连续介质力学理论提出了一种热塑性树脂基体与碳纤维机织物的叠层模型。与单独采用碳纤维机织物超弹性本构模型预测CFRTP成型性能的方法相比,提出的叠层模型能够表征成型温度、压边力和纤维取向对CFRTP成型缺陷的影响,并能优化热冲压成型工艺参数。这一叠层模型具有简单实用和材料参数容易确定的优点,为碳纤维机织物增强热塑性树脂复合材料成型的数值模拟和成型工艺优化奠定了理论基础。     

Nomex Kevlar平纹织物超高速撞击本构模型开发

为了研究Nomex-Kevlar平纹织物对空间碎片的超高速撞击力学特性, 运用LS-DYNA本构模型二次开发技术开发了Nomex-Kevlar平纹织物在超高速撞击条件下的带最大应力失效标准的线弹性正交各向异性本构模型, 并定义了Nomex-Kevlar平纹织物在超高速撞击条件下的Gruneison状态方程参数。运用光滑粒子流体动力学方法和有限元方法建立了与NASA试验工况相同的Al-2017-T4球形弹丸以6.84km/s速度斜向30°撞击Nomex-Kevlar平纹织物的数值分析模型。仿真结果与试验结果的比较表明, 本文中开发的本构模型以及建立的数值分析模型可以准确描述Nomex-Kevlar平纹织物的超高速撞击力学特性。      

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。      

Woven fabric composites—part I: Predictions of homogenized elastic properties and micromechanical damage analysis

In Part 1, the finite element developments are described to first predict the homogenized elastic properties of woven fabric composites, followed by a progressive damage analysis for the subsequent investigation of micromechanical damage initiations and propagations in the representative unit cell of woven fabric composites. For progressive damage analysis, in‐plane uniaxial tensile and shear loading are applied, respectively, to the unit cell. In order to make the boundaries of the unit cell remain straight, displacement control loading is applied instead of force control loading. The tensile and shear stress–strain curves are obtained and shown to be in good agreement with available experimental results. Utilizing the computational efforts in Part 1, the characterization of macro‐crack initiation loads is carried out in Part 2 for the global damage analysis without the need to resorting to experimental data for the prediction of damaged properties. Copyright © 2001 John Wiley & Sons, Ltd.     

Loosely woven fabric model with viscoelastic crimped fibres for ballistic impact simulations

A computational micro‐mechanical material model of loosely woven fabric for non‐linear finite element impact simulations is presented in this work. The model is a mechanism incorporating the crimping of the fibres as well as the trellizing. The equilibrium of the mechanism allows the straightening of the fibres depending on the fibre tension. The contact force at the fibre crossover point determines the rotational friction dissipating a part of the impact energy. The stress–strain relationship is viscoelastic based on a three‐element model. The failure of the fibres is strain rate dependent. The model is implemented as user defined subroutine in the transient finite element code LS‐DYNA. The ballistic impact simulations with the model are in good agreement with the experimental results. Copyright © 2004 John Wiley & Sons, Ltd.     

A micromechanical model for interpenetrating multiphase composites

The dependence relation between the macroscopic effective property and the microstructure of interpenetrating multiphase composites is investigated in this paper. The effective elastic moduli of such composites cannot be calculated from conventional micromechanics methods based on Eshelby’s tensor because an interpenetrating phase cannot be extracted as dispersed inclusions. Employing the concept of connectivity, a micromechanical cell model is presented for estimating the effective elastic moduli of composites reinforced with either dispersed inclusions or interpenetrating networks. The model includes the main features of stress transfer of interpenetrating microstructures. The Mori–Tanaka method and the iso-stress and iso-strain assumptions are adopted in an appropriate manner of combination, rendering the calculation of effective moduli quite easy and accurate.     

A micromechanical model for kink-band formation: Part I — Experimental study and numerical modelling

The initiation and propagation of kink-bands are investigated through an experimental study and numerical modelling. Based on the results achieved, the sequence of events and key features for kink-band formation are identified; particularly, matrix yielding is found to play a crucial role in the process, and fibres are found to fail in the compressive side first. The findings from both the experimental and numerical programmes show a remarkable agreement, and are further applied to the development of an analytical model (Part II of this paper) for kink-band formation.     

A model for ballistic impact on multi-layer fabric targets

An analytical model has been developed in this paper for the ballistic impact behavior of two-dimensional woven fabric composites of interest in body armor applications.     

Computational micro‐mechanical model of flexible woven fabric for finite element impact simulation

This work presents a computational material model of flexible woven fabric for finite element impact analysis and simulation. The model is implemented in the non‐linear dynamic explicit finite element code LSDYNA. The material model derivation utilizes the micro‐mechanical approach and the homogenization technique usually used in composite material models. The model accounts for reorientation of the yarns and the fabric architecture. The behaviour of the flexible fabric material is achieved by discounting the shear moduli of the material in free state, which allows the simulation of the trellis mechanism before packing the yarns. The material model is implemented into the LSDYNA code as a user defined material subroutine. The developed model and its implementation is validated using an experimental ballistic test on Kevlar woven fabric. The presented validation shows good agreement between the simulation utilizing the present material model and the experiment. Copyright © 2001 John Wiley & Sons, Ltd.     

A modified micromechanical curved beam analytical model to predict the tension modulus of 2D plain weave fabric composites

This paper proposes a new analytical solution to predict the elastic modulus of a 2D plain weave fabric (PWF) composite accounting for the interaction of orthogonal interlacing strands. The two orthogonal yarns in a micromechanical unit cell are idealized as curved beams with a path depicted by using sinusoidal shape functions. The modulus is derived by means of a strain energy approach founded on micromechanics. Four sets of experimental data pertinent to four kinds of 2D orthogonal PWF composites have been implemented to validate the new model. The calculations from the new model are also compared with those by using four models in the earlier literature. It is shown that the experimental results correlate well with predictions from the new model.     

A corotational interpolatory model for fabric drape simulation

Fabric drapes are typical large displacement, large rotation but small strain problems. In particle models for fabric drape simulation, the fabric deformation is characterized by the displacements of the particles distributed over the fabric. In this paper, a new particle model based on the corotational concept is formulated. Under the small membrane strain assumption, the bending energy can be approximated as a quadratic function of the particle displacements that are finite. In other words, the tangential bending stiffness matrix is a constant and only the tangential membrane stiffness matrix needs to be updated after each iteration or step. On the other hand, the requirement on the particle alignment is relaxed by interpolating the particle displacement in a patch of nine particles. To account for the membrane energy, a simple and efficient method similar to the three‐node membrane triangular element employing the Green strain measure is adopted. With the present model, the predicted drapes appear to be natural and match our daily perception. In particular, circular clothes and circular pedestal that can only be treated laboriously by most particle models can be conveniently considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Linear thermoviscoelasticity. Part I: A functional model

Summary A functional model is proposed to account for the evolution of linear thermoviscoelastic media. By suitably modelling the fading memory of the medium, several quantities associated with this memory are defined, particularly under cyclic loading. Comparisons are made between this model and various existing thermomechanical constitutive equations: The assumptions implicitly involved in the latter are explicitly stated and the reservations they call for are discussed in the light of experimental data.     

Recrystallization of 30Cr2Ni4MoV ultra-super-critical rotor steel during hot deformation. Part I: Dynamic recrystallization

This paper presents an investigation that characterizes the evolution of the dynamically recrystallized structure of 30Cr2Ni4MoV ultra-super-critical rotor steel during hot deformation, as a starting point for studies of the static recrystallization (SRX) and the metadynamic recrystallization (MDRX) behaviors, by hot compression tests which are performed at the temperatures from 1243 K to 1543 K and strain rates from 0.001 s⁻¹ to 0.1 s⁻¹ on Gleeble-3500 thermo-mechanical simulator, and the corresponding flow curves are obtained. A third-order polynomial is then fitted to the work hardening region of each curve. The critical stress for initiation of dynamic recrystallization (DRX) can be calculated by setting the second derivative of the third order polynomial. By regression analysis, the activation energy in whole range of deformation temperature is determined to be Q = 368.45 kJ/mol. The complete DRX grain size (D_drx) of the test steel is a function of Zener-Hollomon parameter (Z) and is independent of the true strain. The relationship of D_drx and Z is found to be described in a form of power law function with an exponent of −0.24.     

A dynamic simulation model for transient absorption chiller performance. Part I: The model

This paper is the first of two which presents the development of a dynamic model for single-effect LiBr/water absorption chillers. The model is based on external and internal steady-state enthalpy balances for each main component. Dynamic behaviour is implemented via mass storage terms in the absorber and generator, thermal heat storage terms in all vessels and a delay time in the solution cycle. A special feature is that the thermal capacity is partly connected to external and partly to internal process temperatures.In this paper, the model is presented in detail. For verification, the model has been compared to experimental data. The dynamic agreement between experiment and simulation is very good with dynamic deviations around 10 s. General functionality of the model and a more detailed comparison with experimental data are presented in Part II of this paper.     

A co‐rotational grid‐based model for fabric drapes

Fabric drapes are typical large displacement, large rotation and small strain problems. Compared to conventional geometric non‐linear shell analyses, computational fabric drape analysis is particularly challenging due to the extremely weak bending rigidities of fabrics. Compared to continuum shell finite element methods, grid‐ or particle‐based methods appear to be more successful in high drapeability problems. The latter methods often resort to simple particle mechanics and formulate the elastic energy in terms of the inter‐particle distances and trigonometrical functions of the angles between the straight lines joining adjacent particles. In this paper, the co‐rotational approach and commonly employed assumptions for small strain problems in finite element analysis will be adopted to formulate the elastic energy. It will be seen that the internal force vector and the stiffness matrix are considerably simpler than other grid‐based models, yet the sparsity of the tangential stiffness matrix remains unchanged. A number of examples are considered and the predicted results are promising. Copyright © 2003 John Wiley & Sons, Ltd.     

A cohesive micromechanic fatigue model. Part I: Basic mechanisms

A model which identifies a cohesive (bonding) reaction between a broken element (molecule, or chain) and its neighbor as the main micro-scale source of fatigue failure, is proposed. By applying statistical laws, the macro response is revealed. Three types of macro damage accumulation functions emerge, in agreement with known experimental, as a direct result of different values for the micro-material parameters. The reference type shows secondary and tertiary stages, the second type includes an additional primary stage, and the third type, exhibiting an endurance limit, has a primary stage only.

A very well known empirical power law relationship between the fatigue stress and the number of cycles to failure is obtained analytically for the reference type, when a Weibull strength distribution function for the micro-elements is used. The micro-scale roots of the model enables the use of physical internal variables for the damage evolution equations. Thus, a clear insight of the macro response, including the existence of an endurance limit, is achieved through basic mechanism on the micro-scale.

Experimental correlations with available fatigue data for different materials, including metals, plastics and composites, show the general validity of the model, in spite of the diversity of their micro-structures.

It may be proposed that in each material type, the physical “element” is different (i.e. molecules for plastics, grains for metals, etc.), but their response towards fatigue is similar: a non-reversible bonding between a broken element and its neighbor.