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

The critical tearing energy and $\text{J-}\text{integral}$ 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 $\text{J}$ values. Specimen geometry affects both fracture characterizing parameters because of the energy dissipated during deformation. However, the $\text{J-}\text{integral}$ analysis can partition this energy between the crack tip region and the bulk of the specimen. Therefore, application of the $\text{J-}\text{integral}$ concept for characterizing fracture of elastomers is promising.     

Influence of seawater and residual stresses on fatigue crack growth in C---Mn steel weld joints

Results are presented on fatigue crack growth of weld joints made of C---Mn structural steel plates in both air and seawater. Tests were conducted to identify the behavior at different locations of the joints as the frequency, R-ratio and electrochemical potential are varied. Residual stresses in specimens with welds are evaluated to analyse the fatigue crack growth behavior. Satisfactory predictions are obtained by accounting for residual stresses and crack closure.     

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.     

Very high cycle fatigue for GCr15 steel with smooth and hole-defect specimens

Very high cycle fatigue (VHCF) properties of a low temperature tempering bearing steel GCr15 with smooth and hole-defect specimens are studied by employing a rotary bending test machine with frequency of 52.5 Hz. Both smooth and hole-defect specimens break in VHCF regime with some difference in fatigue crack initiation. For smooth specimens, a fine granular area (FGA) is observed near the grain boundary in the fracture surface of the specimens broken after 10⁷ cycles. But no FGA is observed in the hole-defect specimens broken in VHCF regime, and the VHCF crack does not initiate from the small hole at the surface as it does at low or high cycle fatigue regime. Internal stress is employed to explain the VHCF behavior of these two types of specimens. At last, an advanced dislocation model based on Tanaka and Mura model is proposed to illustrate the internal stress process and to predict fatigue crack initiation life with FGA observed in the fracture region.     

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.     

Scaling of size/time/temperature — Part 2: Progressive damage in uniaxial compressive specimen

This work is concerned with predicting the fatigue failure initiation of a wing/fuselage bolt assembly. Accounted for in the analysis are both the influence of energy dissipation and damage accumulation as the structure is subjected to repeated cyclic loading. Results involving the location and number of cycles to initiate a fatigue crack 10⁻² in. are obtained. They agreed both qualitatively and quantitatively with the experimental findings. Also discussed is the influence of pre-torque in the bolt which tends to decrease the number of cycles to fatique crack initiation. Fatigue life may be extended by altering the load path so as to decrease the accumulation of energy near the site of failure initiation. This can be accomplished without major modification of the design. The methodology that makes use of the strain energy density criterion can be used to optimize the fatigue strength of other structural sub-assemblies by appropriate combination of material and geometry for specified load conditions.     

基于非齐次复合Poisson过程的正交异性钢桥面板细节疲劳裂纹随机扩展研究

传统的正交异性钢桥面板疲劳损伤评估常采用确定性和可靠性分析方法,忽略了疲劳裂纹扩展的随机性影响,针对这一问题,提出钢桥面板细节疲劳随机扩展分析方法。本文以南溪长江大桥为工程背景,基于长期车辆荷载监测数据,建立了车辆荷载非齐次复合Poisson过程模型。建立钢桥面板有限元模型,采用瞬态分析方法将随机车辆荷载转化成细节疲劳应力,基于线弹性断裂力学理论推导U肋-顶板焊接细节疲劳裂纹扩展时变微分方程,实现宏观关系式疲劳应力幅次数-疲劳损伤至微观表达式应力时间序列-疲劳损伤转换,讨论了车载次序及超载对疲劳裂纹扩展的影响。研究结果表明,非齐次复合泊松过程模型能够较好描述随机车流运营状态,车辆荷载的次序对疲劳裂纹扩展速率的影响不可忽略,重车排序靠前时能够促使疲劳裂纹扩展增速,南溪长江大桥细节点的车辆超载迟滞效应修正系数取值0.804。     

The role of grain boundaries on fatigue crack initiation - An energy approach

In this paper, we construct a model for prediction of fatigue crack initiation based on the material’s microstructure. In order to do so, the energy of a persistent slip band (PSB) is monitored and an energy balance approach is taken, in which cracks initiate and the material fails due to stress concentration from a PSB (with respect to dislocation motion). These PSBs are able to traverse low-angle grain boundaries (GB), thus belonging to clusters of grains. As a consequence of the ongoing cyclic slip process, the PSBs evolve and interact with high-angle GBs, the result of which leads to dislocation pile-ups, static extrusions in the form of ledges/steps at the GB, stress concentration, and ultimately crack initiation. Hence, this fatigue model is driven by the microstructure, i.e. grain orientations, widely distributed grain sizes, precipitates, PSB-GB interactions, as well as the affect of neighboring grains. The results predict that cracks initiate near twin boundaries from PSBs spanning a single large grain with a favorable orientation or multiple grains connected by low-angle GBs. Excellent agreement is shown between model predictions and experimental data.     

Finite Fracture Mechanics model for mixed mode fracture in adhesive joints

Up to now the failure load assessment of bonded joints is still not fully understood. This work provides a new approach for assessing the crack initiation load of bonded joints. A failure model for single lap joints is proposed that is based on Finite Fracture Mechanics. Only two basic fracture parameters are required: the tensile strength and the fracture toughness of the adhesive. A coupled stress and energy criterion proposed in 2002 by Leguillon is used to model crack initiation in the adhesive layer. The theory of this criterion is outlined in detail, its relationship to other failure criteria is discussed and an overview of applications found in literature is given. An enhanced weak interface model that predicts a linear variation of the shear stresses in the adhesive layer is utilized to model the single lap joint. To compare joint designs and to reveal the limitations of the given approach a dimensionless brittleness number for mixed-mode loading is proposed. Along with a detailed discussion of the results for exemplary joint designs a comparison to experimental results from literature is performed. The two necessary fracture parameters are each taken from standard test results published in literature. A good agreement of the failure load predictions with the experimental results is observed. A remarkable outcome is that the presented failure model renders the adhesive thickness effect correctly. The paper concludes with a discussion of the limitations of the approach and the effect of material parameters.     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

Numerical and experimental determination of three-dimensional multiple crack growth in fatigue

This work is concerned with the assessment of propagation of multiple fatigue cracks in three-dimensions. Computational modelling of fatigue crack propagation is made together with detection and monitoring of the crack shape development. The boundary element method (BEM) is used for automating the modelling of crack propagation in linear elastic as well as elastic–plastic regimes. Strain at several positions on the specimen surface near the crack mouth is measured to monitor crack initiation, shape development and closure levels. Examples are provided to validate the model by comparing the experimental results with those obtained by numerical predictions.     

Initiation and propagation of fatigue crack in pure aluminium single crystals

The fatigue crack initiation and propagation in the pure aluminum single crystals with different orientations are investigated. Acoustic Emission (AE) technique is used to monitor the fatigue crack initiation and propagation data. The results show that the acoustic emission technique could be used for detecting fatigue crack initiation and propagation. The total counts of AE are plotted as a function of the number of fatigue cycles, and change in slope of the curve corresponded to the initiation of the fatigue crack. The fatigue crack initiation and propagation are related to the specimen crystalline orientation. Specifically, they depend on the ratio K of the Schmid factor of the secondary slip system, to that of the primary one. The greater the ratio K, the easier the fatigue crack initiates and the faster the fatigue crack propagates. When the ratio K is equal or close to one, the fatigue crack grows either along a cleavage plane which intersects both the primary plane and the secondary one or along the primary slip plane and the secondary one. Growth along alternating planes can also occur giving rise to a zigzag path. When the ratio K is much less than one, the fatigue crack grows along the primary slip plane only. The results are explained with a model for the faceted mode of fatigue crack growth.     

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

Crack initiation direction from interface of bonded dissimilar media

Debonded region of an interface between two dissimilar materials are modeled as a line crack that tends to enhance the initiation of failure by fracture. Depending on the load that interacts with dissimilar materials, no a priori knowledge of how failure would initiate from an existing interface crack is assumed. By application of the strain energy density criterion, potential crack initiation sites are obtained for different biaxial loading states and materials with dissimilar properties.Numerical results are obtained for an epoxy/aluminum medium. In each case, a finite line segment of debonding is assumed. Uniform stresses are applied normal and parallel to the interface so that a biaxial load factor k determines the relative magnitude of biaxiality. Positive and negative k correspond, respectively, to applied tension and compression parallel to the interface. For a fixed ratio of the elastic moduli, crack initiation angles measured from the interface would increase with positive k and decrease with an increase of negative k. These findings are presented for different values of k. The direction of maximum yield initiation could also be determined from the stationary values of the strain density function. These locations are identified with elements that undergo excessive distortion while the possible fracture sites are assumed to coincide with regions where dilatational effects would dominate.     

沥青混合料疲劳过程的损伤力学分析

采用损伤力学方法研究沥青混合料的疲劳失效问题。针对悬壁梁弯曲疲劳试件,推导出疲劳过程中应力场、损伤场和疲劳裂纹形成寿命的工程封闭公式。根据沥青混合料特点,提出一种模拟疲劳裂纹扩展的特征单元失效模式,从而将疲劳裂纹形成与扩展两个阶段统一用损伤力学理论进行描述和分析。本文对沥青混合料试件的疲劳裂纹形成寿命与扩展寿命分段进行了预测,还对疲劳过程中刚度衰减及位移幅值的演化过程进行了数值模拟计算。理论预期与实验结果吻合良好。     

Rheology of suspensions of spherical particles in a newtonian and a non-newtonian fluid

Properties of suspensions of spherical glass beads (25–38 μm dia.) in a Newtonian fluid and a non-Newtonian (NBS Fluid 40) fluid were measured at volume fractions, φ, of 0%, 10%, 20% and 30%. Measurements were made using a modified and computerized Weissenberg Rheogoniometer. Properties measured included steady shear viscosity, η($\text{γ}\text{.}$), first normal stress difference, N₁($\text{γ}\text{.}$), linear viscoelastic properties, η′(ω) and G′(ω), shear stress relaxation, σ^? ($\text{γ}\text{.}$, t), and growth, σ⁺($\text{γ}\text{.}$, t) and normal stress relaxation, N₁^?($\text{γ}\text{.}$, t).For a the Newtonian fluid, increasing φ causes both η and η′ to increase, with η′ showing a slight frequency dependence. Both N₁ and G′ are zero and stress relaxation and growth occur essentially instantaneously. For the NBS fluid, both η and η′ increse with φ at all $\text{γ}\text{.}$ and ω, respectively, the increase being greater as $\text{γ}\text{.}$ and ω approach zero. N₁ and G′ are less affected by the presence of the particles than η and η′ with the effect on G′ being more pronounced than on N₁. For fixed $\text{γ}\text{.}$, stress relaxation and growth exhibit greater non-linear effects as φ is increased. A model for predicting a priori the linear viscoelastic properties for suspensions was found to yeild reasonable estimates up to φ = 20%.     

近场动力学框架下钢轨疲劳裂纹萌生预测的数值方法研究

经典连续介质力学在求解由裂纹引起的不连续问题时，会出现数学构架失效的情况. 为克服这一难题，基于近场动力学理论，构建铁路钢轨疲劳裂纹萌生的数值预测方法，可实现钢轨疲劳裂纹萌生寿命与位置的预测. 当未出现疲劳裂纹时，通过与经典连续介质力学模型的结果对比，验证近场动力学模型的正确性和适用性. 分析了车轮全滑动、黏着-滑动和无摩擦三种状态对钢轨疲劳裂纹萌生的影响规律，结果表明:车轮由全滑动向无摩擦转变的过程中，裂纹萌生位置由钢轨表层转移到内部，裂纹萌生所需的荷载循环次数由0.45×107次增至2.05×107次，可见车轮滚滑状态会影响裂纹的萌生位置，并且较大的切向接触应力会显著降低钢轨的疲劳裂纹萌生寿命.      

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.