Meso-Scale Finite Element Simulations of 3D Braided Textile Composites: Effects of Force Loading Modes

Meso-scale finite element method (FEM) is considered as the most effective and economical numerical method to investigate the mechanical behavior of braided textile composites. Applying the periodic boundary conditions on the unit-cell model is a critical step for yielding accurate mechanical response. However, the force loading mode has not been employed in the available meso-scale finite element analysis (FEA) works. In the present work, a meso-scale FEA is conducted to predict the mechanical properties and simulate the progressive damage of 3D braided composites under external loadings. For the same unit-cell model with displacement and force loading modes, the stress distribution, predicted stiffness and strength properties and damage evolution process subjected to typical loading conditions are then analyzed and compared. The obtained numerical results show that the predicted elastic properties are exactly the same, and the strength and damage evolution process are very close under these two loading modes, which validates the feasibility and effectiveness of the force loading mode. This comparison study provides a suitable reference for selecting the loading modes in the unit-cell based mechanical behavior analysis of other textile composites.     

An RVE-based micromechanical analysis of fiber-reinforced composites considering fiber size dependency

An RVE-based micromechanical elastic damage model considering fiber size dependency is presented to predict the effective elastic moduli and interfacial damage evolution in fiber-reinforced composites. To assess the validity of the present model, the predictions based on the proposed micromechanical elastic model are compared with Hashin’s theoretical bounds [Hashin Z. Analysis of properties of fiber composites with anisotropic constituents. J Appl Mech: Trans ASME 1979;46:543–50]. The proposed micromechanical elastic damage model is then exercised under uniaxial loading conditions to show the overall elastic damage behavior of the proposed micromechanical framework and to illustrate fiber size effect on the behavior of the composites. Moreover, comparisons between the present prediction and experimental data are made to further illustrate the capability of the proposed micromechanical framework for predicting the elastic damage behavior of fiber-reinforced composites.     

High-order nonlinear contact effects in cyclic loading of delaminated sandwich panels

The interaction between the delaminated surfaces and its influence on the static and on a special type of cyclic load behavior of delaminated sandwich panels is studied. In addition, the results for a cyclic push–pull load and the analysis for the detection of damage in sandwich panels is presented. The analysis uses the high-order theory of sandwich panels (HSAPT) and considers geometrical nonlinear effects and the nonlinearity associated with the contact characteristics of the delaminated surfaces. The nonlinear contact phenomena, which are associated with variation of the contact conditions during motion, result in differences in the stiffness of the delaminated panel, which are detected under a push or pull type of loads. Quantitative assessment of these differences sheds light on the existence, size, and location of the delaminated region and can be used for a nondestructive evaluation of the damage characteristics of the delaminated panel. The field equations and the corresponding boundary and continuity conditions of the nonlinear analytical model are derived via the variational principle of virtual work. The mathematical formulation uses the ordinary unidirectional panel theory for the face-sheets and a two-dimensional elasticity approach for the core. It yields a set of nonlinear differential equations that are solved using the Multiple Shooting Method combined with a Newton–Raphson iterative scheme. The influence of the nonlinear contact phenomena on the behavior of the panel under two loading schemes is numerically studied. The first loading scheme is a push–pull loading simulation that demonstrates the concept of the proposed damage detection method. The second loading scheme simulates the conditions that evolve during free vibration response. The results reveal the role of the nonlinear contact phenomena in the cyclic bending behavior of the sandwich panel and its influence on the localized and overall nonlinear response. A summary and conclusions close the paper.     

复合材料单钉接头疲劳累积损伤破坏分析

基于时间增量原理 , 推导了层合板接头疲劳加载累积损伤应力2应变分析的虚功方程。同时 , 引入Hashin三维疲劳失效准则进行材料的损伤判定 , 并结合建立的疲劳加载材料退化模型、 4种基本损伤机制相互关联作用的材料性能退化方法及复合材料接头最终失效判据 , 建立了层合板接头疲劳载荷作用下三维累积损伤分析的寿命预测方法。最后 , 对层合板接头拉2拉疲劳载荷作用下的损伤累积扩展与失效规律进行了仿真分析 , 并与试验结果进行了对比 , 结果表明 : 本文中建立的寿命预测方法能够很好地预测层合板接头的寿命以及损伤发生、扩展及最终失效。      

Damage development under gradual loading of composites

We present a theoretical investigation of damage development in Ceramic Matrix Composites (CMC's) before catastrophic failure under gradual loading conditions. The aim of the work is to give a theoretical interpretation of the experimental results on the development of damage in the C/C-SiC composite obtained by cyclically loading, unloading, and reloading a planar specimen. Our approach is based on statistical, micromechanical models of the failure of CMC's in the framework of global load sharing, where the failure mechanism includes quasi-periodic matrix cracking, gradual breaking of fibers, and sliding of broken fibers with respect to the matrix. It is demonstrated that the non-linear characteristics of the constitutive behavior and the potential drop measured under uniaxial loading of a planar C/C-SiC specimen can be described with reasonable accuracy in the framework of statistical, micromechanical models.     

Description of fatigue damage in carbon black filled natural rubber

The present paper describes macroscopic fatigue damage in carbon black‐filled natural rubber (CB‐NR) under uniaxial loading conditions. Uniaxial tension‐compression, fully relaxing uniaxial tension and non‐relaxing uniaxial tension loading conditions were applied until sample failure. Results, summarized in a Haigh‐like diagram, show that only one type of fatigue damage is observed for uniaxial tension‐compression and fully relaxing uniaxial tension loading conditions, and that several different types of fatigue damage take place in non‐relaxing uniaxial tension loading conditions. The different damage types observed under non‐relaxing uniaxial tension, loading conditions are closely related to the improvement of rubber fatigue life. Therefore, as fatigue life improvement is classically supposed to be due to strain‐induced crystallization (SIC), a similar conclusion can be drawn for the occurrence of different types of fatigue damage.     

The choice of cyclic plasticity models in fatigue life assessment of 304 and 1045 steel alloys based on the critical plane-energy fatigue damage approach

The present study intends to examine various cyclic plasticity models in fatigue assessment of 304 and 1045 steels based on the critical plane-energy damage approach developed earlier. Cyclic plasticity models of linear hardening, nonlinear, multi-surface, and two-surface were chosen to study fatigue damage and life of materials under proportional and non-proportional loading conditions. The effect of additional hardening induced due to non-proportional loading in 1045 steel and particularly in 304 steel was further evaluated as different constitutive models were employed. In the present study, the plasticity models were calibrated by the equivalent cyclic stress–strain curves. The merits of the models were then investigated to assess materials deformation under proportional and non-proportional loading conditions. Under non-proportional loading, the cyclic plasticity models were found to be highly dependent upon the employed hardening rule as well as the materials properties/coefficients.The stress and strain components calculated through constitutive laws were then used as input parameters to evaluate fatigue damage and assess the fatigue life of materials based on the critical plane-energy approach.The calculated values of stress components based on constitutive laws resulted in a good agreement with those of experimentally obtained under various loading paths of proportional and non-proportional conditions in 1045 steels. In 304 steel, the calculated stress components were however found in good agreement when plasticity models were employed for proportional loading conditions. Under non-proportional loading, the application of the multi-surface plasticity model in conjunction with the fatigue damage approach resulted in more reasonable results as compared with other plasticity models. This can be attributed to the motion of the yield surface in deviatoric stress space in the multi-surface model encountering additional hardening effect through estimated higher stress values under non-proportional loading conditions.Predicted fatigue lives based on the critical plane-energy damage approach showed such range of agreements as ±1.05–±3.0 factors in 1045 and 304 steels as compared with experimental life data when various constitutive plasticity models were employed.     

Fatigue resistance of natural rubber in seawater with comparison to air

Fatigue properties of filled natural rubber in seawater environment are investigated by uniaxial fatigue and crack propagation experiments, and the damage is analyzed by scanning electron microscopy. The behavior under relaxing and non-relaxing loading conditions is studied and the results are compared to those obtained in air environment. For relaxing loading conditions, fatigue behavior is the same in both environments. Under non-relaxing conditions at large strain levels, for which the influence of strain-induced crystallization is important, fatigue life is longer in seawater. Such behavior could be explained by increased internal temperatures of specimens tested in air due to lower heat conductivity of air as compared to seawater. Such conclusion is also supported by the damage mechanisms observed under non-relaxing loading conditions.     

两级蠕变下损伤演变及寿命估算

在两级或多级加载下,材料的蠕变寿命分数之和与加载顺序密切相关,这表明加载历史对损伤演变过程具有显著的影响。本研究采用考虑损伤和硬化影响的蠕变律,得到了蠕变损伤演变过程受加载历史的影响,讨论了两组蠕变加载时损伤演变和寿命估算问题。总结表明,本方法与试验结果吻合较好,可以反映加载效应的影响。     

Nondestructive Testing and Prediction of Remaining Fatigue Life of Metals

A nondestructive testing method is presented for the prediction of the remaining fatigue life (RFL) of metals with prior fatigue damage subjected to tension-compression fatigue load. It is shown that the slope of temperature rise obtained from a short-time excitation fatigue test is a good candidate to assess the present state of fatigue damage in the material. Three series of uniaxial tension-compression normal fatigue tests are carried out with two different materials under different loading conditions to characterize their fatigue behavior. Eight validation tests are performed under different loading conditions to evaluate the RFL prediction capability of the proposed method. Results show that the proposed method has good potential for predicting RFL of metallic specimens.     

Shape control and damage identification of beams using piezoelectric actuation and genetic optimization

This paper deals with the shape control of beams under general loading conditions, using piezoelectric patch actuators that are surface bonded onto beams to provide the control forces. The mathematical formulation of the model is based on the shear deformation beam theory (Timoshenko theory) and the linear theory of piezoelectricity. The numerical solution of the model is based on the development of superconvergent (locking-free) finite elements using the form of the exact solution of the Timoshenko beam theory and Hamilton’s principle. The optimal values for the locations of the piezo-actuators are determined and optimal voltages for shape control are obtained for cantilever beams by using a genetic optimization procedure. Finally, a simplified related damage identification problem is formulated and solved using static data and genetic optimization.     

基于微观力学失效理论的CFRP多向层合板低速冲击行为预测

基于微观力学失效(MMF)理论对碳纤维增强复合材料(CFRP)多向层合板在低速冲击载荷下失效机制及损伤过程进行分析和预测。建立基于MMF理论的层合板结构冲击损伤行为分析方法。首先, 使用MMF理论对冲击过程中组分的失效类别进行判别; 然后, 根据组分失效的类别制定出相应的材料性能退化方案来实现对复合材料在低速冲击下的逐步失效分析;在ABAQUS平台上开发了基于显示分析的用户材料子程序(VUMAT), 即基于MMF理论的层合板冲击损伤分析程序;最后, 利用MMF理论冲击损伤行为分析方法, 对UTS50/E51碳纤维增强复合材料多向层合板在小能量低速冲击情况下的失效机制和损伤形貌进行预测, 并将预测结果与试验结果进行对比, 分析了利用MMF理论预测冲击损伤这一方法的准确性。结果表明理论预测的凹坑直径与试验测试的凹坑直径误差为4.8%, 预测的失效机制和损伤形貌与实际观察的一致。      

A nonuniform hardening plasticity model for concrete materials

For the most part, the developments of constitutive models for for the concrete by the theory of plasticity have in the past been made to scarch for a suitable failure surface. The initial yield surface is usually assumed to have the same shape as the failure surface but with a reduced size. The subsequent loading surfaces are then obtained by the uniform expansion of the initial one. This approach is found generally inadequate in predicting the deformational behavior of concrete for a wide range of loading conditions.

The present non-uniform hardening plasticity model adopts the most sophisticated failure model of Willam-Warnke or Hsieh-Ting-Chen as the bounding surface; assume an initial yield surface with a shape that is different from the failure surface; proposes a nonuniform hardening rule for the subsequent loading surfaces with a hydrostatic pressure and Lode-angle dependent plasticity modulus; and utilizes a nonassociated flow rule for a general formulation.

The work-hardening stress-strain behaviors of concrete based on the present model are found in good agreement with experimental results involving a wide range of stress states and different types of concrete material. The important features of inelastic behavior of concrete, including brittle failure in tension; ductile behavior in compression; hydrostatic sensitivities; and volumetric dilation under compressive loadings can all be represented by this improved constitutive model.     

FATIGUE DAMAGE IN 1045 STEEL UNDER CONSTANT AMPLITUDE BIAXIAL LOADING

The progressive nature of fatigue damage under multiaxial stress states has been investigated. Experiments were performed on thin-wall tubular specimens of 1045 steel in tension, torsion and combined tension-torsion loading. Two equivalent strain amplitudes, one in the high cycle fatigue (HCF) region and one in low cycle fatigue (LCF) region were employed in this study. Four recently proposed damage theories were evaluated. Crack depth was used as a damage parameter in comparing damage curves under different loading modes.
Different types of crack systems were observed in the HCF and LCF regions. The damage curve obtained in tension loading can be used to evaluate the damage behavior under combined tension—torsion loading. The results of torsion loading show that torsional damage behavior is different from the above two loading modes.     

A non-proportional loading finite element analysis of continuum damage mechanics for ductile fracture

This paper presents the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non-proportional loading. The condition of non-proportional loading is formulated by introducing a dynamic co-ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly. The finite element analysis developed under non-proportional loading is applied to predict the crack initiation load of a centre-cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre-cracked thin plates made of aluminium alloy 2024-T3. The analysis also reveals under non-proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.     

Time-Dependent Deformation and Damage Growth in a Rubber-Toughened Fiber Composite

Time-dependent deformation and damage growth was studied in arubber-toughened carbon fiber composite. Cyclic creep/recovery loading wasperformed on unidirectional off-axis coupons to derive the transverse andshear moduli. Constant stress-rate experiments were also performed usingmodal acoustic emission monitoring. This monitoring provides indirectevidence of what is believed to be the primary damage mechanisms in thematerial studied, matrix cracking and fiber/matrix debonding.Three significant findings from this study are emphasized in this paper.The first is the viscoelastic and viscoplastic behavior of the material withgrowing damage. Although a complete characterization has not beenperformed, emphasis is on material behavior believed to be not previouslyreported in the literature. The second is a new Damage Effect Study thatquickly identifies the material parameters in a nonlinear viscoelasticconstitutive theory that are affected by damage. This study can assist instreamlining the characterization process. Finally, a simplified materialmodel for the microstructure is developed based on AE monitoring of damagegrowth. This results in damage evolution equations based on AE data andviscoelastic fracture mechanics. The damage equations correlate AE data fordifferent loading histories. The use of direct monitoring to develop damageevolution equations and the Damage Effect Study reflect a new approach tocharacterization testing of time-dependent materials.