The behavior of cracked cross-ply composite laminates under shear loading

An interlaminar-shear-stress analysis developed earlier by Tsai et al. (1990, Micro-cracking-Induced Damage in Composites) for a [φ_m/θ_n], bi-directional composite laminate is used to solve the case of a cross-ply [0_m/90_n]_x laminate with the 90° layer only or both layers cracked under pure shear loading. Strains, forces and laminate shear modulus reduction due to matrix cracking were obtained. Experimental results for shear modulus as a function of crack densities were obtained by a simple shear test and they agree very well with the theoretical prediction.     

Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

We analyze approximate approaches to the modeling of the thermomechanical behavior of physically nonlinear materials under harmonic loading. The approaches are based on various harmonic-linearization schemes and the concept of complex moduli. Mechanical and mathematical features of various schemes are considered. Some modifications of the model are proposed to account for various aspects of material behavior under harmonic loading. The problems of vibration and dissipative heating of physically nonlinear bodies are formulated. The main thermomechanical characteristics are analyzed for some classes of problems.The study was partially sponsored by the State Fund for Basic Research of the Ministry of Education and Science of Ukraine (Grant No. 01.07/00050).Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–34, September 2004.     

Experimental study of changes in the fluid structure under constant shear loading

Experiments are performed to study the change in the fluid structure that decreases the effective viscosity of samples of a high-viscosity polar fluid (glycerin) and a polymer (Plexiglas) under shear loading. Empirical relations are proposed for estimating the behavior of viscosity decreasing in the course of loading versus time and governing parameters of the system.     

Failure loads of spot weld specimens under impact opening and shear loading conditions

Failure loads of spot weld specimens are investigated under impact combined loading conditions. A set of test fixtures was designed and used to obtain failure loads of mild steel spot weld specimens under combined opening and shear loading conditions. Three different impact speeds were applied to examine the effects of separation speed on failure loads. Micrographs of the cross-sections of failed spot welds were obtained to understand the failure processes in mild steel specimens under different impact combined loads. The experimental results indicate that the failure mechanisms of spot welds are very similar for mild steel specimens at various impact speeds. These micrographs show that the sheet thickness can affect the failure mechanisms. For 1.0 mm specimens, the failure occurs near the base metal in a necking/shear failure mode. For 1.5 mm specimens, the failure occurs near the heat-affected zone in a shear failure mode. Based on the experimental results, the effects of the inertia force, the separation speed, and the loading angle on the failure loads of spot welds are investigated. Failure criteria are proposed to characterize the failure loads of spot welds under impact combined opening and shear loads for engineering applications. The failure load can be expressed as a function of the tensile strength of the base metal, the nugget size, the sheet thickness, the maximum separation speed, the loading angle, and empirical coefficients for a given welding schedule.     

Generalized Maxwell model for the viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading

The linear viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading is investigated in the glass transition range. Using the time-temperature superposition technique, the master curves of the shear dynamic relaxation moduli are obtained at a reference temperature of 566°C. A method to determine the viscoelastic constants from dynamic relaxation moduli is proposed. However, some viscoelastic constants cannot be directly measured from the experimental curves and others cannot be precisely obtained due to non-linearity effects at very low frequencies. The generalized Maxwell model is investigated from the experimental dynamic moduli without fixing the viscoelastic constants. A set of parameters is shown to be in good agreement with the experimental dynamic relaxation moduli, but does not give the correct values of the viscoelastic constants of the investigated glass. The soda-lime-silica glass exhibits a non-linear viscoelastic behavior at very low stress level which is usually observed for organic glasses. This non-linear behavior is questioned.     

Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

酚醛层压材料的冲击力学行为及本构模型

为了研究酚醛层压材料的冲击力学行为并获得本构模型,利用万能试验机和整形修正的分离式霍普金森压杆(SHPB)装置,对材料试样进行了应变率范围为10^-3~10³ s^-1的单轴压缩实验,得到了不同加载应变率下的应力应变曲线,对其在准静态、动态载荷下的压缩破坏机理进行了初步探讨。结果表明,酚醛层压材料具有较强的应变率效应,与准静态(1.67×10^-3 s^-1)时相比,在动态载荷(7×10² s^-1)下,峰值应力增加了约10倍;破坏应变减少了约一半;在准静态和动态加载条件下试样力学性能的差异是由于纤维基体界面特性以及不同应变率下破坏模式的不同;采用朱-王-唐本构方程描述了酚醛层压材料力学行为,拟合得到了本构方程的系数,在加载过程中,理论计算值与实验结果吻合较好。

     

岩体-界面系统剪切不稳定性分析

基于界面的刚塑性应变软化假设,分析了岩体－界面系统在端部剪力和岩体中分布剪切载荷共同作用下的变形、应力和损伤演化。利用位能原理和稳定性的能量准则,得到了岩体界面系统的不稳定性条件。分析结果表明,损伤区达到边界之前,系统可能是稳定的或者是不稳定的。依赖于分布剪切载荷和界面摩擦力的比较,若均布剪切载荷大于界面摩擦力,则系统不稳定,否则系统稳定;当损伤区达到边界之后,系统的不稳定性决定于载荷及界面材料性质,界面软化刚度系数和界面强度对于不稳定性有明显影响。     

Failure surface of epoxy-modified fiber-reinforced composites under transverse tension and out-of-plane shear

The mechanical behavior of uniaxially fiber-reinforced composites with a ductile rubber-toughened epoxy matrix was studied through the finite element analysis of a RVE of the composite microstructure. The fibers were represented by elastic and isotropic solids, while the rubber-modified epoxy matrix behaved as a elasto-viscoplastic solid. The matrix flow stress followed the model developed by Jeong [Jeong, H.-Y., 2002. A new yield function and a hydrostatic stress-controlled void nucleation model for porous solids with pressure-sensitive matrices. International Journal of Solids and Structures 39, 1385–1403.], which included the inherent pressure-sensitivity of the yield stress in the epoxy matrix, the damage due to the cavitation of the rubber particles and subsequent void growth, and the particular features of elastic–viscoplastic behavior in glassy polymers, particularly the intrinsic softening upon yield followed by hardening. Composites with either perfect or weak fiber/matrix interfaces (the latter introduced through cohesive elements) were studied to assess the influence of interface strength on the composite behavior. Simulations under transverse tension and out-of-plane shear were carried out to establish the effect of loading conditions on the dominant deformation and failure micromechanisms. In addition, the corresponding failure locus was obtained and compared with the predictions of current phenomenological failure criteria for composites. The range of validity of these criteria and the areas for further improvement were established by comparison with the numerical results.     

Non-uniqueness and stability of two-family fiber-reinforced incompressible hyper-elastic sheet under equibiaxial loading

The problems on the non-uniqueness and stability of a two-family fiber- reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configu- rations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain criticM value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.     

The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Summary In this paper, the behavior of a crack in functionally graded piezoelectric/piezomagnetic materials subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using a Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. These equations are solved using the Schmidt method. The relations among the electric displacement, the magnetic flux and the stress field near the crack tips are obtained. Numerical examples are provided to show the effect of the functionally graded parameter on the stress intensity factors of the crack.The authors are grateful for financial support from the Natural Science Foundation of Hei Long Jiang Province (A0301), the National Natural Science Foundation of China (50232030, 10172030), the Natural Science Foundation with Excellent Young Investigators of Hei Long Jiang Province(JC04-08) and the National Science Foundation with Excellent Young Investigators (10325208).     

Crack problem under shear loading in cubic quasicrystal

IntroductionQuasicrystalasanewstructureofsolidmatter[1,2 ]bringsprofoundnewideastothetraditionalcondensedmatterphysicsandencouragesconsiderabletheoreticalandexperimentalstudiesonthephysicalandmechanicalpropertiesofthematerial,includingtheelasticitytheoryofthequasicrystal,manyvaluableresultsweregiven[3～ 5 ].Defectsinthematerialwereobservedsoonafterthediscoveryofthequasicrystal[6 ,7].Cracksareonetypeofdefects,theirexistencegreatlyinfluencesthephysicalandmechanicalpropertiesofthequasicrystalinem…     

Three-dimensional elliptic crack under impact loading

The dynamic stress intensity factor of a three-dimensional elliptic crack under impact loading is determined with the finite element method. The computation results can take into account the influence of time and the ratio of the wave speeds on the stress intensity factor. The present method is suitable not only for three-dimensional dynamic crack, but also for three-dimensional dynamic contact. Project supported by the National Natural Science Foundation of China (No. K19672007).     

Analysis of reinforced-concrete strength under impact loading

A mathematical model is proposed to describe deformation and fracture of reinforced concrete under impact loading within the framework of mechanics of continuous media. The problem of the impact of steel cylindrical projectiles on rectangular slabs made of reinforced concrete is solved. The results of mathematical modeling are in good agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 165–173, November–December, 2006.     

Motion of soil-working tool under impact loading

The cyclic process of penetration of soil by a tool under periodic impact loading was described mathematically. The analysis was based on a piecewise-linear approximation of the dependence of the soil frontal resistance force on tool displacement—an approximation reflecting modern views on the principles of soil-tool interaction.Different intervals in the cycle of steady-state motion of the tool, and different interaction regimes were considered. The mean tool velocity for borehole forming was determined. Conditions for a minimum energy requirement in the cyclic process were formulated, and the influence of frequency on the laws governing the interaction was established.     

Dynamic plastic behavior of structures under impact loading investigated by the extended hamilton's principle

We propose the extended Hamilton's principle to investigate the dynamic plastic behavior of a beam or a plate under an impact loading. Material is assumed to be rigid perfectly plastic. The impact loading is given in the form of initial velocity. Good agreement between our numerical solutions and experimental results done by Parkes and Jones indicates that the proposed variational method is a powerful approximation method for the dynamic plasticity analysis. The effect of strain-rate sensitivity on the permanent deflection of a plate is investigated in some detail. Instead of nonlinear differential equations, nonlinear algebraic equations are solved in the proposed method.     

Fracture dynamics problems of orthotropic solids under anti-plane shear loading

By application of the approaches of the theory of complex functions, fracture dynamics problems of orthotropic solids under anti-plane shear loading were researched. Universal representation of analytical solutions was obtained by means of self-similar functions. The problems dealt with can be facilely transformed into Riemann–Hilbert problems by this technique, and analytical solutions of the stress, the displacement and dynamic stress intensity factor under the actions of moving increasing loads Px ²/t ² and Pt ³/x ² for the edges of asymmetrical mode III crack, respectively, were acquired. In the light of corresponding material properties, the variable rule of dynamic stress intensity factor was illustrated very well.     

The yield of mild steel under impact loading

Results are given of impact tests on mild steel specimens using a method of test described in a previous paper. A dynamic stress-strain curve is derived which indicates that the upper and lower yield stresses are about double those obtaining under normal static conditions. The results are compared with those of other investigators.