Crack bifurcation in laminar ceramics having large compressive stress

Crack bifurcation is observed in laminar ceramics that contain large residual compressive stress. In such composites, alternating material layers have tensile and compressive residual stress, due to thermal expansion mismatch or other sources. The compressive stress ensures that crack growth leading to failure in the laminar system is mediated by threshold strength, but, in some cases, it also leads to bifurcation of the propagating flaw. The phenomenon of bifurcation takes place when the crack tip is propagating in the compressive layer, and occurs typically at a distance equal to a few laminate thicknesses below the free surface and beyond. The observation of this phenomenon is usually associated with the presence of edge cracking in the compressive layers of the laminar ceramic, although it can also occur in the absence of such edge cracks. In the few cases where bifurcation occurs without edge cracks, the residual stresses and layer thicknesses are close to the condition in which edge cracks will occur. In addition, in this case the bifurcation is confined to near the specimen free surface, and below the bifurcation plane, the cracks are straight. The energy release rates for the straight and bifurcated cracks are calculated from the results of finite element computations and compared. When edge cracking is ignored, the crack is simulated as a through-thickness crack in an infinite body, and the energy release rate is used to predict crack deviation and bifurcation. Based on this, the finite element model successfully predicts bifurcation in only one material combination that was investigated in experiments. However, the experimental bifurcation takes place in two additional material combinations. When the effect of edge cracking is incorporated into the finite element simulations, the energy release rate calculations successfully predict the phenomenon of bifurcation in three material combinations, as observed in the experiments. Since no edge cracks are present in the fourth material combination tested experimentally, its lack of bifurcations is automatically predicted by the model. The presence of edge cracking, or its incipience, is thus concluded to be critical to the occurrence of crack bifurcation in laminar ceramic composites.     

Edge-cracked bimaterial systems under thermal heating

The problem of thermoelastic edge-cracking in two-layered bimaterial systems subjected to convective heating is considered. The medium is assumed to be insulated on one surface and exposed to sudden convective heating on another surface containing the edge crack. It is known that, when a bimaterial system’s surface is heated, compressive stresses arise near the heating surface, forcing the crack surfaces together over a certain cusp-shaped contact length. It is also known that, for a cooled bimaterial systems surface, tensile stresses take place close to the cooling surface and tend to open the crack. So, the edge cracked heating surface problem is treated as an embedded crack with a smooth closure condition of the crack surfaces, with the crack contact length being an additional unknown variable. Superposition and uncoupled quasi-static thermoelasticity principles are adopted to formulate the problem. By using a Fourier integral transform technique, the mixed boundary value problem is reduced to a Cauchy type singular integral equation with an unknown function as the derivative of the crack surface displacement. The numerical results of the stress intensity factors for an edge crack and a crack terminating at the interface, are calculated and presented as a function of time, crack length, heat transfer coefficient, and thickness ratio for two different bimaterial systems, namely a stainless steel layer welded on ferritic steel and a ceramic layer coating on ferritic steel.     

Thermo-mechanical solution of film/substrate systems under local thermal load and application to laser lift-off of GaN/sapphire structures

Film/substrate structures may undergo a localized thermal load, which can induce stresses, deformation and defects. In this paper, we present the solutions of temperature and stresses in a film/substrate structure under a local thermal load on the film surface. Then, the generalized Stoney formula, which connects the curvature of deformation and the stress field is obtained. The present solution takes into account the non-uniformity of the temperature field both in the width and thickness directions of the film. The thermo-mechanical solution is applied to the analysis of the temperature distribution, stresses, and damage of a GaN/sapphire system during the laser lift-off (LLO) process. It is shown that the laser with the Gaussian distribution of energy density causes much smaller tensile stresses at the edge of the heated area in the film than the laser with the uniform distribution of energy density, and thus can avoid damage to the GaN films separated from the substrate.     

Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior

A contact stress analysis is presented for a layered elastic half-space in contact with a rough surface exhibiting self-affine (fractal) behavior. Relationships for the mean contact pressure versus representative strain and the real half-contact width versus elastic properties of the layer and the substrate, asperity radius, layer thickness, and truncated half-contact width were derived from finite element simulations of a layered medium compressed elastically by a rigid cylindrical asperity. These relationships were incorporated in a numerical algorithm that was used to obtain the contact pressure distributions and stresses generated by the asperity contacts formed at the interface of the layered medium and the fractal surface. Analytical solutions illustrate the significance of the elastic material properties, layer thickness, and surface topography (roughness) on global parameters such as normal load and real contact area. Results for the contact pressure distribution and the surface and subsurface stresses provide insight into the initiation of yielding and the tendency for cracking in the layered medium. It is shown that cracking at the surface and the layer/substrate interface is more likely to occur in the case of a stiff layer, whereas surface cracking is more prominent for a relatively compliant layer.     

Cracking mechanisms in lithiated silicon thin film electrodes

The massive cracking of silicon thin film electrodes in lithium ion batteries is associated with the colossal volume changes that occur during lithiation and delithiation cycles. However, the underlying cracking mechanism or even whether fracture initiates during lithiation or delithiation is still unknown. Here, we model the stress generation in amorphous silicon thin films during lithium insertion, fully accounting for the effects of finite strains, plastic flow, and pressure-gradients on the diffusion of lithium. Our finite element analyses demonstrate that the fracture of lithiated silicon films occurs by a sequential cracking mechanism which is distinct from fracture induced by residual tension in conventional thin films. During early-stage lithiation, the expansion of the lithium-silicon subsurface layer bends the film near the edges, and generates a high tensile stress zone at a critical distance away within the lithium-free silicon. Fracture initiates at this high tension zone and creates new film edges, which in turn bend and generate high tensile stresses a further critical distance away. Under repeated lithiation and delithiation cycles, this sequential cracking mechanism creates silicon islands of uniform diameter, which scales with the film thickness. The predicted island sizes, as well as the abrupt mitigation of fracture below a critical film thickness due to the diminishing tensile stress zone, is quantitatively in good agreement with experiments.     

Interaction of an edge dislocation with a coated elliptic inclusion

This paper presents an analytical solution for plane elasticity problems of an elliptically cylindrical layered media subject to an arbitrary edge dislocation. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the displacements and stresses, where an edge dislocation is located in matrix, coating layer and inclusion are obtained. The numerical results of image forces exerted on a generalized edge dislocation are carried out by using the generalized Peach–Koehler equation. As a numerical illustration, both the image forces and equilibrium positions are presented for different material combinations and relative thickness of a coating layer. The result shows that the thickness and the shear modulus of the coating layer have a strong influence on the stability of dislocation.     

Stress fields and Eshelby forces on half-plane inhomogeneities with eigenstrains and strip inclusions meeting a free surface

The stress field due to a half-plane inhomogeneity with plane eigenstrain is obtained by a limiting procedure from the one of a circular Eshelby inhomogeneity/inclusion. This field, which requires tractions to be applied at infinity to be sustained, has minimum strain energy versus any other superposed homogeneous one, and is the Eshelby solution inside plus the Hill jump conditions. By superposition, the stresses due to an infinite strip (Eshelby property domain) inhomogeneity with eigenstrain are obtained, and, by superposition periodic strips or laminates can be obtained. By cancelling the stresses on a free-surface, strips of inclusions meeting a free surface are solved. They exhibit tensile stresses under the free surface, and logarithmic singularities in the tensile stress at the vertex, which may initiate cracking. The Eshelby self-forces on the boundary of circular and half-plane inhomogeneities are computed.     

异质双材料粘接梁的界面端部应力及端部龟裂破坏的实验应力分析

本文采用了高灵敏度的云纹干涉法对异质双材料粘接梁在弯曲载荷作用下的位移进行了测量，用局部杂交法对界面端部区域的应变和应力进行了计算。通过对该区域内的实验应力分析发现：拉应力σｘ是影响结构强度的关键因素。本文还对在基体材料表面近角点区域可能出现的龟裂破坏的原因进行了分析。     

Supersonic flow around the trailing edge of a thin profile

The method of mergeable asymptotic expansions has recently been used effectively in investigations devoted to the study of boundary layer interaction with an external inviscid flow at high subcritical Reynolds numbers Re. The asymptotic analysis permits obtaining a limit pattern of the flow around a solid as Re þ, and determining the similarity and quantitative regularity laws which are in good agreement with experimental results. Thus by using the method of mergeable asymptotic expansions it is shown in [1–4] that near sites with high local curvature of the body contour and flow separation and attachment points, an interaction domain appears that has a small length on the order of Re^-3/8. In this flow domain, which has a three-layer structure, the pressure distribution in a first approximation already depends on the change in boundary-layer displacement thickness, while the induced pressure gradient, in turn, influences the flow in the boundary layer. An analogous situation occurs in the neighborhood of the trailing edge of a flat plate where an interaction domain also appears [5, 6]. The flow in the neighborhood of the trailing edge of a flat plate around which a supersonic viscous gas flows was examined in [7]. Numerical results in this paper show that the friction stress on the plate surface remains positive everywhere in the interaction domain, and grows on approaching the trailing edge. The supersonic flow around the trailing edge of a flat plate at a small angle of attack was investigated in [8, 9], Supersonic flow of a viscous gas in the neighborhood of the trailing edge of a flat plate at zero angle of attack is examined in [10], but with different velocity values in the inviscid part of the flow on the upper and lower sides of the plate. The more general problem of the flow around the trailing edge of a profile with small relative thickness is investigated in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 36–42, May–June, 1981.     

Fracture and buckling of thin panels with edge crack in tension

This study is concerned with the buckling and/or cracking of thin aluminium panels with an edge crack in tension. Two types of end conditions are considered. In the first case, the ends of the panel are clamped such that they would extend in parallel. In the second case, the ends are permitted to rotate when extended in tension. The cracked edge would open while the smooth edge is compressed that could lead to out-of-plane deflection if the panels are sufficiently thin. An empirical relation is obtained for the critical tensile stress. Relations among the geometrical parameters for which buckling occurs are also derived.     

Modeling the evolution of stress due to differential shrinkage in powder-processed functionally graded metal–ceramic composites during pressureless sintering

Pressureless sintering of powder-processed functionally graded materials is being pursued to economically produce metal–ceramic composites for a variety of high-temperature (e.g., thermal protection) and energy-absorbing (e.g., armor) applications. During sintering, differential shrinkage induces stresses that can compromise the integrity of the components. Because the strength evolves as the component is sintered, it is important to model how the evolution of the differential shrinkage governs the stress distribution in the component in order to determine when the strength will be exceeded and cracking initiated. In this investigation, a model is proposed that describes the processing/microstructure/property/performance relationship in pressurelessly sintered functionally graded plates and rods. This model can be used to determine appropriate shrinkage rates and gradient architectures for a given component geometry that will prevent the component from cracking during pressureless sintering by balancing the evolution of strength, which is assumed to be a power law function of the porosity, with the evolution of stress. To develop this model, the powder mixture is considered as a three-phase material consisting of voids, metal particles, and ceramic particles. A micromechanical thermal elastic–viscoplastic constitutive model is then proposed to describe the thermomechanical behavior of the composite microstructure. The subsequent evolution of the thermomechanical properties of the matrix material during sintering is assumed to obey a power law relationship with the level of porosity, which is directly related to the shrinkage strain, and was refined to account for the evolving interparticle cohesion of the matrix phase due to sintering. These thermomechanical properties are incorporated into a 2-D thermomechanical finite element analysis to predict the stress distributions and distortions that arise from the evolution of differential shrinkage during the pressureless sintering process. Differential shrinkage results were verified quantitatively through comparison with the shape profile for a pressurelessly sintered functionally graded nickel–alumina composite plate with a cylindrical geometry, and the stress distribution results verified from qualitative observations of the absence or presence of cracking as well as the location in specimens with different gradient architectures. The cracking was mitigated using a reverse gradient at one end of the specimen, and the resulting distortions associated with the shape profile were determined to be no more than 15% reduced from the predictions. The effects of geometry were also studied out-of-plane by transforming the plate into a rod through an increase in thickness, while in-plane effects were studied by comparing the results from the cylindrical specimen with a specimen that has a square cross-sectional geometry. By transforming from a plate to a rod geometry, the stress no longer exceeds critical levels and cracks do not form. The results from the in-plane geometric study indicated that critical stresses were reached in the square geometry at temperatures 100 °C less than in the cylindrical geometry. Additionally, the location of primary cracking was shifted towards the metal-rich end of the specimen, while the stress distribution associated with this shift and the lower temperature for the critical stress resulted in secondary cracking.     

Stress intensity factor for an edge crack in two bonded dissimilar materials under convective cooling

The transient thermal stress crack problem for two bonded dissimilar materials subjected to a convective cooling on the surface containing an edge crack perpendicular to the interface is considered. The problem is solved using the principle of superposition and the uncoupled quasi-static thermoelasticity. The crack problem is formulated by applying the transient thermal stresses obtained from the uncracked medium with opposite sign on the crack surfaces to be the only external loads. Fourier integral transform is used to solve the perturbation problem resulting in a singular integral equation of Cauchy type in which the derivative of the crack surface displacement is the unknown function. The numerical results of the stress intensity factors are calculated for both the edge crack and the crack terminating at the interface using two different composite materials and illustrated as a function of time, crack length, coefficient of heat transfer, and the thickness ratio.     

Creep in concrete beams strengthened with composite materials

This paper investigates the creep behaviour of concrete beams strengthened with externally bonded composite materials. The challenges associated with the creep modelling of the different materials involved are discussed and a theoretical model is developed. The model derived in the paper accounts for the viscoelasticity of the materials using differential-type constitutive relations that are based on the linear Boltzman’s principle of superposition. The model also accounts for the deformability of the adhesive layer in shear and through its thickness, and for its ability to resist stresses in these directions. These aspects are not fully accounted for in the existing models. An incremental formulation of the field equations is conducted via the variational principle of virtual work, which considers the variation of the internal stresses in time and their effect on the creep response. A numerical study that examines the capabilities of the model and quantifies the response of the strengthened beam to sustained loads is presented, with special focus on the edge stresses that develop at the adhesive interfaces and which initiate debonding failures. The effect of flexural cracking of the concrete is also considered through an enhancement of the model, along with a numerical example that describes the variation with time of the forces and stresses in the concrete beam, the internal steel reinforcement, and the FRP strip at the cracked section.     

Free-edge stresses and progressive cracking in surface coatings of circular torsion bars

This paper considers the explicit solutions of free-edge stresses near circumferential cracks in surface coatings of circular torsion bars and their application in determining the progressive cracking density in the coating layers. The problem was formulated within the framework of linear elastic fracture mechanics (LEFM). The free-edge stresses near crack tip and the shear stresses in the cross-section of the torsion bar were approached in explicit forms based on the variational principle of complementary strain energy. Criterion for progressive cracking in the coating layer was established in sense of strain energy conservation, and the crack density is thereby estimated. Effects of external torque, aspect ratio, and elastic properties on the density of progressive cracking were examined numerically. The present study shows that, in the sense of inducing a given crack density, compliant coating layer with lower modulus has much higher critical torque than that of a stiffer one with the same geometries and substrate material, i.e., compliant coating layer has greater cracking tolerance. Meanwhile, the study also indicates that thicker surface coating layer is more pliant to cracking than the thinner ones. The present model can be used for analyzing the damage mechanism and cracking tolerance of surface coatings of torsion shafts and for data reduction of torsional fracture test of brittle surface coatings, etc.     

Impact damage of laminated composite with energy dissipation: Part II — Damage evolution

Having developed the methodology for analyzing the failure of a ceramic/rubber/steel composite laminate impacted by a tungsten rod in Part I, Part II of the work is concerned with the progressive damage process where material continuity would be interrupted at different locations and time intervals. Depending on the time rate dependent threshold values of the surface and volume energy density, the degree and extent of damage by fragmentation, mass loss, etc. are determined by finite element calculations for time steps of 0.15, 5.0, 7.5, 10, 20, 21 and 21.5 μs. Stresses and strains possess an oscillatory character in time; they alternate in sign as the impact waves bounce back and forth in the three-layered dissimilar materials.Local strain rates of approximately 10⁵, 10³ and 10⁴ s⁻¹ are formed in the ceramic, rubber and steel layer respectively at locations underneath the tungsten rod after 16 μs of impact. A more wide range of strain ratio would have prevailed for a homogeneous layer of the same thickness. The tungsten rod is now badly fragmented while cracking near the surface of the ceramic is also predicted. Local temperature and dissipation energy density rise rapidly as time approached 20 μs. The maximum surface and volume.energy density in the ceramic near the impact region reached 260 MPa · m and 6.39 MPa, respectively. Complete disintegration of the tungsten rods occurred at 21.5 μs. At this time, the ceramic layer is perforated and the rubber layer is partially cracked. The back-up steel plate, however, remained in tack. These predictions agree qualitatively with past observations.     

氧化锆增韧陶瓷与A95陶瓷抗侵彻性能对比实验研究

使用穿甲弹对两种陶瓷材料,10%氧化锆增韧陶瓷和A95陶瓷,开展了系列弹道实验研究。分析了各自的抗弹防护系数随射弹入射速度的变化规律,并分析了材料强度和韧性对其抗侵彻性能的影响。实验表明:两种陶瓷材料的质量防护系数都明显高于1,但在射弹入射速度为1000.0~1300m/s的范围内,A95陶瓷靶的抗侵彻能力高于增韧陶瓷的抗侵占能力。随着入射速度的提高,增韧陶瓷的抗侵彻能力提高的更快,并在某点出现转折入射速度以上,大约1300m/s,其与A95陶瓷的抗侵彻能力趋于相同,显示了增韧陶瓷在抗高速侵彻方面的适用性。     

Subcritical crack growth of edge and center cracks in façade rock panels subject to periodic surface temperature variations

This paper examines subcritical cracking in a rock panel or slab containing either a pre-existing edge or a center crack perpendicular to the panel surface. The panel is subject to periodic surface temperature variation on one side of the panel while the other is kept at a constant temperature. The thermally induced stress intensity factors are determined using superposition technique by employing the fundamental point load solution for an edge crack or a center crack in a slab of finite thickness. Rock panel is modeled as a long elastic strip with either a free or a fully constrained lateral end condition. The temperature variations versus time at various depths of the rock panel appear roughly as a sinusoidal function. The lateral thermal stress for the free end case is larger than the constrained end case; whereas stress intensity factors for both edge and center cracks in the constrained end slab are 1000 times larger than that of free end case. Subcritical crack propagation in rock panels on façade is then estimated as a function of time. This subcritical crack propagation continues until a critical crack size is attained and the rock panel will fail under wind load. This new theoretical framework provides a new paradigm to examine the mechanisms of time-dependent cracking in rock panels on façade of buildings.     

Spherical ceramic pebbles subjected to multiple non-concentrated surface loads

This paper presents an analytical solution for the stress distributions within spherical ceramic pebbles subjected to multiple surface loads along different directions. The method of solution employs a displacement approach together with the Fourier associated Legendre expansion for piecewise boundary loads. The solution corresponds to spherically isotropic elastic spheres. The classical solution for isotropic spheres subjected diametral point loads is recovered as a special case of our solution. For the isotropic pebbles under consideration, stresses within spheres are numerically evaluated. The results show that the number of loads does have significant influence on the maximum tensile stress inside the sphere. Moreover, the applicability of solutions using the series expansion method for stresses near surface load areas is also examined. The stresses evaluated with large enough number of terms agree quite well with those derived from FEM simulations, except around the edge of circle load area.     

Stress intensity factors and crack initiation directions for ceramic/metal joint

Four points bending tests for Si₃N₄/Cu/S45C joint specimen showed that the bending strengths depend on the residual stresses that originated from joining process. The residual thermal stresses caused an edge sub-interface crack to initiate in the ceramic. The stress intensity factors (SIFs) of the edge sub-interface crack located at distance h from the interface with or without interlayer metal were calculated by the Green's function obtained from a finite element analysis. The crack path at the joint specimen under four points bending loading with the influence of residual stresses was also evaluated by the maximum tensile stress criterion. Finally the effect of residual stress on the crack path was found numerically; the interlayer metal decreases the deflection angle of crack from interface by reducing the residual stress.