Critical J-integral and tearing energies for fracture of reinforced natural rubber

The critical tearing energy and J-integral for initiation and rapid crack propagation at 22°C were determined for carbon black reinforced natural rubber. Tearing energies were 20 per cent and up to 100 per cent greater for initiation and rupture, respectively, and more scattered than the J values. Specimen geometry affects both fracture characterizing parameters because of the energy dissipated during deformation. However, the J-integral analysis can partition this energy between the crack tip region and the bulk of the specimen. Therefore, application of the J-integral concept for characterizing fracture of elastomers is promising.     

Plane-strain deformation near a slot extended under load: Some observations using grain-orientated 312per cent silicon-iron

Experiments were performed using grain-orientated $\text{3}\text{1}\text{2}$per cent silicon-iron. Plane-strain deformation can be obtained in thin plates of this material and, also, the plastic deformation that occurs can be revealed by etching. In some experiments the slot was extended while the specimen was under load and the plastic deformation was then observed. The distribution and density of the resulting slip-lines agrees qualitatively with J. R. Rice's (1968) model of the deformation at the tip of a crack growing in a continuum. In Rice's model, irreversible plastic deformation prevents complete focusing of the slip-lines at a crack tip; and in the present work an analogous effect was observed, the major difference being that in the present experiments the slip-lines are fixed by the crystal structure of the material. A qualitative explanation of the observations is given in terms of the interaction that exists between dislocations and a crack.     

Constant amplitude and variable load history fatigue test results and predictions for cruciform and lap welds

Cruciform and lap welds were fatigue tested under constant amplitude axial load and SAE Bracket spectrum load conditions. For the cruciform joints, fatigue cracks generally initiate at the root but may initiate at the toe if higher bending stresses are induced by joint distortion. For lap welds, the stress ratio ($\text{R}$) and weld shape are the major factors influencing the fatigue crack initiation site.The fatigue test results were compared with predictions made using an analytical model developed by the authors, and good agreement between experiment and theory was observed. The model for the predictions assumes that the fatigue crack initiation period, which is the number of cycles for the initiation of a fatigue crack and its early growth and coalescence into a dominant fatigue crack, is the main portion of the total fatigue life at long lives.     

The role of shear stresses in brittle fracture

Using the three-dimensional model for brittle fracture developed earlier by S.A.F. Murrell and P.J. Digby (1970,1972) shear stress concentrations are calculated for brittle bodies and the relative roles of tensile and shear stresses in the fracture process are considered. It is found that the maximum shear stress and the maximum tensile stress occur at different places on a crack, and that there is a wide range of stress states for which they do not occur on the same crack. Furthermore, if the theoretical cleavage strength is σ_max and the theoretical shear strength is τ_max, then cleavage precedes inelastic shear and brittle fracture is possible, for suitable stress systems, when $\text{σ}{}_{\max }\text{<}\text{2τ}{}_{\mathrm{<mtext>max</mtext>}}\text{(1 ? ν)}$, where ν is the Poisson's ratio of the solid matrix. This appears to be in accordance with empirical observations.     

An analysis of the fracture initiation of falling type impact test for toughened rigid plastics

A quasi-static linear viscoelastic model for the dart impact type test on toughened rigid plastics is proposed and analysed. Based on the modified Maxwell element model of viscoelastic behavior of material with relaxation modulus E(t) = E_f + (E_o ? E_f)e${}^{\mathrm{<mtext>?t</mtext><mtext>t</mtext><mtext>R</mtext>}}$, some approximate computations are performed to assess the relative importance of various parameters such as the impact velocity, fracture initiation.energy and critical stress.     

A path-independent integral for fracture of solids under combined electrochemical and mechanical loadings

In this study, we first demonstrate that the J-integral in classical linear elasticity becomes path-dependent when the solid is subjected to combined electrical, chemical and mechanical loadings. We then construct an electro-chemo-mechanical J-integral that is path-independent under such combined multiple driving forces. Further, we show that this electro-chemo-mechanical J-integral represents the rate at which the grand potential releases per unit crack growth. As an example, the path-independent nature of the electro-chemo-mechanical J-integral is demonstrated by solving the problem of a thin elastic film delaminated from a thick elastic substrate.     

A line plastic-zone model for steady mode III crack growth in an elastic-plastic material

Steady-state quasi-static growth of a crack in the anti-plane shear mode through an elastic-plastic material is analyzed. The material is non-hardening and small-scale yielding conditions are assumed. The essential feature of the model is that the active plastic-zone is assumed to be a pair of discrete lines emanating from the crack tip out of the crack plane on which a suitable yield condition is satisfied. An exact solution is obtained for the plastic strain left in the wake of this active line plastic-zone. The extent of the plastic zone from the tip is determined to be 0.071 $\text{(}\text{k}\text{τ}{}_0\text{)}{}^2$ where k and τ₀ are the remote elastic stress intensity factor and the shear flow stress, respectively, and it is found that 36% of the elastic energy flowing into the crack-tip region during growth is dissipated through plastic work and 64% is trapped as residual elastic energy in the plastic-zone wake.     

An elastic-plastic analysis of an asymmetric cracked specimen subjected to longitudinal shear

Some recent elastic-plastic analyses of cracked specimens subjected to symmetric mode III loading are extended to include asymmetric loading and geometry. Solutions are given for arbitrary work hardening behaviour in any specimen that is amenable to a linear elastic analysis. It is shown that asymmetry has a major influence on the shape of the plastic zone, but does not affect the J-integral unil the loading is well into the large scale yielding range. In particular the “plastic zone corrected” estimate of J, obtained by elastically solving a problem for a crack longer than the actual one, is shown to remain a valid two-term asymptotic expansion in the presence of asymmetry. The general results are applied to a crack at an angle to a uniform stress field in a power law hardening material. The growth of the plastic zone is displayed graphically for various hardening exponents and crack orientations. No other asymmetric solution is available, but values of J are compared with those obtained from a fully plastic analysis in the symmetric case.     

Size effect of cylindrical specimens with fatigue cracks

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., $\text{ΔS}\text{Δa}\text{=}\text{const}$. Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Stable growth of fracture in brittle aggregate materials

Fracture of concrete is analyzed by combining the resistance curve (R-curve) approach with linearly elastic solutions for the energy release rate resulting from the quasi-static crack model of Wnuk, analogous to the D-BCS model of a stationary crack used in describing quasi-brittle fracture in metals. The R-curve, representing the crack length dependence of the energy consumed per unit fracture extension, is calculated using the concept of the energy separation rate associated with a finite crack growth steps. To simplify calculations, the tensile stress transmitted across the nonlinear zone ahead of the fracture front is assumed to be uniformly distributed over the entire nonlinear zone, even though in reality it must be a gradually declining stress resulting in strain-softening; and an infinite elastic medium loaded at infinity is assumed. These assumptions permit an easy solution with the help of Green's function for an infinite elastic medium. Application to bodies of finite size then requires assuming the nonlinear zone (fracture process zone) to be negligible with regard to specimen dimensions, crack length and ligament length. Even though this assumption is not always realistic, the end results, which are of practical importance, appear reasonable. The analysis leads to a nonlinear first-order ordinary differential equation for the R-curve, which is integrated numerically. The R-curves calculated in this manner can be closely fitted to data from previous fracture tests. Only two parameters, characterizing the initial and the final lengths of the nonlinear zone, need to be adjusted to test data.     

Pressure drop during forced convection boiling of binary refrigerant mixtures

An experimental investigation was carried out in an electrically heated horizontal tube to measure pressure drop for various flow rates and heat fluxes during forced convection boiling of pure refrigerant 12 and four compositions of refrigerants 13 and 12 mixtures. The Martinelli-Nelson correlation, using the properties of the flowing refrigerant mixture, could not predict satisfactorily the pressure drop data. Total, as well as frictional pressure drops were found to be function of concentration. Two separate models each for total, as well as frictional pressure drop were developed for predicting the corresponding pressure drop. In each case, the maximum per cent deviation between predicted and measured pressure drop was within $\text{± 30\%}$.     

Exact solution of the non-linear differential equation RR̈ + 32R2 − AR−4 + B = 0

The non-linear equation $\text{R}\text{R}\text{?}\text{+}\text{3}\text{2}\text{R}{}^2\text{- AR}{}^{\mathrm{?4}}\text{+ B = 0}$ is shown to represent simply periodic motion with a minimum at R₁ and a maximum at R₁R₀ or a maximum at R₁ and a minimum at R₁R₀^?1. R₀ is a function of the ratio $\text{A}\text{B}$ and is greater than 1 for $\text{A}\text{B}$ > 1 and less than 1 for $\text{A}\text{B}$ > 1. The period of the motion satisfies the simple relation T(R₀^?1) = R₀^?1T(R₀). The exact solution to the above equation is represented in terms of elliptic integrals of the first and second kinds and a simple algebraic function.     

采用压缩单裂纹圆孔板确定岩石动态起裂、扩展和止裂韧度

爆炸、冲击、地震等人为或自然灾害不可避免,经常造成大量土木工程设施的破坏,因此岩石在动态载荷作用下的行为受到特别关注.岩石动态断裂韧度是评价岩石抵抗裂纹动态起裂、扩展和止裂性能的材料参数,开展岩石动态断裂韧度测试方法的研究对相关理论基础和实验技术的要求较高.岩石动态断裂韧度分为动态起裂、动态扩展、动态止裂三种,虽然关于动态起裂和动态扩展的研究已有一些成果,对岩石动态止裂的研究仍是一个难题,至今几乎无人问津.研究表明,在分离式霍普金森压杆撞击压缩单裂纹圆孔板岩石试样的I型动态断裂试验中,动态起裂、扩展、止裂的全过程可以由黏贴在压缩单裂纹圆孔板试样上的裂纹扩展计监测,岩石的动态起裂、扩展、止裂韧度可以用实验-数值-解析法确定.特别值得一提的是首次测出了岩石的动态止裂韧度.裂纹扩展计信号还显示,压缩单裂纹圆孔板在止裂后,停止的裂纹还会再次动态起裂、扩展并超出裂纹扩展计的检测范围.从能量的角度分析了动态止裂的过程,指出测试动态止裂韧度时要注意的一些问题.结果显示,岩石动态起裂韧度和动态扩展韧度分别随动态加载率和裂纹扩展速度的增大而增大,岩石动态起裂韧度略大于动态止裂韧度.      

Failure instability of a debonded interface in the presence of a main crack

The problem of fracture initiating from an edge crack in a nonhomogeneous beam made of two dissimilar linear elastic materials that are partially bonded along a common interface is studied by the strain energy density theory. The beam is subjected to three-point bending and the unbonded part of the interface is symmetrically located with regard to the applied loading. The applied load acts on the stiffer material, while the edge crack lies in the softer material. Fracture initiation from the tip of the edge crack and global instability of the composite beam are studied by considering both the local and global stationary values of the strain energy density function, dW/dV. A length parameter l defined by the relative distance between the maximum of the local and global minima of dW/dV is determined for evaluating the stability of failure initiation by fracture. Predictions on critical loads for fracture initiation from the tip of the edge crack, crack trajectories and fracture instability are made. In the analysis the load, the length of the edge crack and the length and position of the interfacial crack remained unchanged. The influence of the ratio of the moduli of elasticity of the two materials, the position of the edge crack and the width of the stiffer material on the local and global instability of the beam was examined. A general trend is that the critical load for crack initiation and fracture instability is enhanced as the width and the modulus of elasticity of the stiffer material increase. Thus, the stiffer material acts as a barrier in load transfer.