Effect of residual stresses on the strength and fracture energy of the brittle film: Multiple cracking analysis

The aim of this paper was to address the effect of the residual stresses within the brittle film on the substrate on the film strength, fracture energy, and interfacial shear strength (IFSS). Special analyses were performed on the SiO_x film/polyethulene terephthalate substrate systems. The residual stresses were evaluated by using the curvature method. The film strength, fracture energy, and IFSS were estimated on the basis of the multiple cracking analyses. In the multiple cracking analyses, the system was subjected to the combination of the residual stresses and the unidirectionally applied stress. Results showed that the relationship between the crack density in the film and the applied strain can be predicted by adopting the energy criterion on the basis of the knowledge on the residual stress distributions in the film segment. The film strength and fracture energy for the initiation of film cracking were almost proportional to the compressive residual stresses in the film. With increasing the compressive residual stresses within the film, the IFSS also increased.     

Note on residual stresses induced by fatigue cracking

A new theoretical model, based on dislocation mechanics, is used here to predict the residual stress distribution resulting from fatique cracking. Photoelastic results which corroborate the analysis perform the basis for some initial assumptions. The associated phenomena of fatigue crack closure is emerged as a by-product. An expression for the residual stress intensity factor ($\text{K}{}_{\mathrm{IR}}$) is derived along with experimental validation.     

Interaction between cyclic loading and residual stresses in titanium matrix composites

Metal matrix composites are gaining popularity for applications where high performance materials are needed. Titanium matrix composites (TMCs) continuously reinforced by silicon carbide fibres are under development for applications in aeroengines. Their use in blades, rings and shafts promises a significant weight reduction and performance improvement due to their high specific strength and stiffness. To obtain the whole capabilities of the material not only advanced processing techniques but also post-processing treatments are necessary. A detailed analysis of the residual stress development during cyclic loading leads to the necessity of residual stress modifications to optimise the fatigue behaviour of TMCs. Since the aerospace industry requires high reliability of the materials used, models for predicting failure and life time are of special interest. Predictive models based on the properties of the single constituents of the composite are most suitable to reduce the number of experiments and to develop methodologies to improve specific mechanical properties. Nevertheless, both experiments on the single constituents as well as on the composite are necessary to validate the model. A previously developed rheological model is used to assess different post-processing procedures to improve the fatigue behaviour of a titanium matrix composite. The usage of the model and experiments on the system SCS-6/Ti-6Al-2Sn-4Zr-2Mo are presented.     

Analytical modeling of residual stresses in multilayered superconductor systems

Residual stresses-induced damages in multilayered films grown on technical substrates present a reliability issue for the fabrication and applications of multilayered superconductor systems. Using closed-form solutions for residual stresses in multilayered systems, specific results were calculated for residual stresses induced by the lattice and the thermal mismatches in the system of YBCO/CeO₂/YSZ/Y₂O₃ films on a Ni-5 W substrate. It was concluded that lattice mismatch-induced residual stresses must be relaxed by forming interfacial defects. Studies of residual thermal stresses showed the following. When the thickness of a film is negligible compared to the substrate, the changes of its properties modify the residual stresses in this film layer but have negligible effects on the residual stresses in other layers in the system. On the other hand, when the thickness of certain film layer is not negligible compared to the substrate, residual stresses in each layer can be controlled by adjusting the properties and thickness of this film layer. Finally, the effects of buffer layers on thermal stresses in YBa₂Cu₃O_7–x (YBCO) were addressed by using YBCO/LaMnO₃/homo-epi MgO/IBAD MgO/Y₂O₃/Al₂O₃ films on Hastelloy substrate as an example.     

Thin film and substrate cracking under the influence of externally applied loads

Cracking in thin film systems subject to residual tension is examined. The existing solution for the case of a crack tip in the substrate is modified to provide a solution of greater accuracy. The influence of external tensile loads on thin film and substrate cracking is examined. An approximate superposition scheme is presented for the determination of the energy release rate. Crack arrest is examined and parameters for determining the possibility of crack arrest are presented. For compliant films it was found that crack arrest does not occur when the substrate stress has the same magnitude as the residual stress. The influence of externally applied loads on crack channelling and conditions under which channelling will occur in the substrate are presented.     

More on the effects of thermal residual and hydrostatic stresses on yielding behavior of unidirectional composites

The influence of manufacturing process thermal residual stresses and hydrostatic stresses on yielding behavior of unidirectional fiber reinforced composites has been investigated when subsequently subjected to various mechanical loadings. Three-dimensional finite element micro-mechanical models have been used. The results of this study reveal that the size of the initial yield surface is highly affected by the thermal residual and hydrostatic stresses. It was also found that effects of a uniform temperature change on the initial yield surface in the composite stress space is not equivalent to a solid translation of the surface in the direction of the hydrostatic stress axis. At the micro-level, magnitudes of various stress components within the matrix due to the thermal residual and hydrostatic stresses are different. However, at a macro-level, both temperature change and hydrostatic loading of composites show similar effects on the initial yield surface in the composite stress space. In an agreement with experimental data, results also show that residual stresses are responsible for asymmetric behavior of composites in uniaxial tension/compression in the fiber direction. This asymmetric behavior suggests that the existing quadratic yield criteria need modification to include thermal residual stress effects.     

Analytical formulae for calculating stresses in unidirectional/cross-ply unbalanced laminates

A multilayer theory has been developed for unidirectional/cross-ply unbalanced laminates subjected to surface shear tractions, using the assumption of plane strain. The analytical solution for the stress field in the laminate is obtained and it is shown that the stresses in each layer are in good agreement with the results of a three-dimensional finite element analysis. Approximate formulae for the analytical stresses are also derived for a laminate subjected to an offset distributed force at one end. The accuracy of this solution is shown by comparison with a three-dimensional finite element analysis.     

Effects of nonuniformity of fiber distribution on thermally-induced residual stresses and cracking in ceramic matrix composites

A three-dimensional finite element analysis is conducted to estimate stresses induced by thermal cooldown in unidirectionally fiber-reinforced ceramic matrix composites. Various configurations of nonuniform fiber distributions are considered. Both cases of thermal expansion mismatch between isotropic, linearly thermoelastic fibers and matrix are studied. Significant effects of nonuniformity of fiber distributions on the local stress states are found. The initiation of various possible cracking modes is discussed in the light of these results.     

Thermal loading of short fibre composites and the induction of residual shear stresses

A study has been undertaken to identify the effect of thermal residual stresses on the stress transfer between a short fibre and resin using the photoelastic method. As expected, it was observed that fibre fracture occurred at a higher applied load for the fibre embedded in the thermally (80 °C) cured epoxy matrix than in the room-temperature-cured epoxy. Under plane polarised light bright birefringent patterns were observed in the hot-cured epoxy matrix around the fibre-ends prior to loading. These were not present in the room-temperature-cured epoxy, indicating that thermal residual stresses had been induced during thermal-curing. On loading, the birefringent patterns in the hot-cured matrix at the fibre-ends were almost extinguished but at a particular stress reappeared as a bright region, and increased in intensity on further loading.Using a phase-stepping polariscope, four images of the fibre-ends were captured simultaneously so that detailed contour maps of fringe order could be created. To examine the micromechanical response in the matrices at the interfaces the profile of interfacial shear stress at the fibre-ends was calculated. Under a given external load the shear stress at the interface in the hot-cured matrix was significantly lower than that in the cold-cured epoxy matrix. The thermal load which is applied to a resin on cooling from manufacture requires a shear stress at the interface to put the fibre into compression. At the fibre-ends a residual shear stress of opposite sign (to that induced mechanically) leads to extension of birefringent patterns on loading.     

Removal of residual stresses by low-temperature annealing to prevent stress-corrosion cracking of carbon steels

The effect of low-temperature annealing on the relaxation of residual stresses and on the stress-corrosion resistance of carbon steels was investigated. It was shown that stress-corrosion cracking of welded joints in carbon steels under the influence of boiling nitrate solutions and alkaline solutions is prevented by annealing at temperatures 450° C and 500° C, respectively.     

Analysis of multiple cracks in thin coating on orthotropic substrate under mechanical and residual stresses

The analysis addresses a typical failure development pattern in thin films consisting of a system of multiple surface cracks leading to and branching along or near the interface between the film and the base material. The process is driven by thermal residual stresses and/or mechanical loading. Due to the high temperature gradients during the fabrication process, usually a net of surface cracks develops, which gives the appearance of a granular structure of the surface. A periodic array of parallel surface cracks is assumed. A “unit cell” or single cracked segment attached to the substrate is analyzed instead by assuming the channel cracks are spaced more or less uniformly and perfectly aligned in parallel in the transverse direction of the coating. The analysis is specialized to orthotropic and transversally isotropic materials. The problem is solved using FEM combined with the reciprocal theorem. Matched asymptotic procedure [Leguillon D, Sanchez-Palencia E. Computation of singular solutions in elliptic problems and elasticity. Paris: Masson; 1987; Vu-Quoc L, Tran VX. Singularity analysis and fracture energy-release rate for composites: piecewise homogenous-anisotropic materials. Comput Methods Appl Mech Engng 2006;195:5162-97] is used to derive the change of potential energy. Higher-order terms in the asymptotics are considered. The competition between penetration and debond for periodically distributed edge cracks especially near the critical value of the ratio of fracture spacing to the layer thickness is examined.     

自支撑金刚石厚膜脱离基体前后的残余应力研究

运用ANSYS软件建立了有限元模型,对直流等离子体喷射制备的自支撑金刚石厚膜在脱离基体前、后的残余应力分别进行了数值模拟。为了使模拟更接近于金刚石膜的真实制备环境,本文取消了以往对金刚石膜或基体内的温度场常作的均匀或线性的人为假设,而采用对从磁控直流等离子体炬内喷射出的射流仿真计算结果。结论如下(:1)金刚石膜脱离基体之前,金刚石厚膜内的热残余应力呈空间应力状态,第一主应力在膜层中心以外的大部分地方均为拉应力,易引起膜开裂破坏;膜/基界面上极大的剪切应力是引起金刚石膜从基体上脱离的主要原因。(2)金刚石膜脱离基体之后,热残余应力绝大部分被释放,膜内最终的残余应力可认为是本征应力。     

Size-dependent elastic properties of unidirectional nano-composites with interface stresses

Summary Surfaces and interfaces in solids may behave differently from their bulk counterparts, particularly when the geometry is on the nanoscale. Our objective in this work is to assess the overall behavior of composites containing cylindrical inclusions with surface effects prevailing along the interfaces. In the formulation, we first decompose the loadings into three different deformation modes: the axisymmetric loadings, the transverse shear and the antiplane shear. For each deformation mode, we derive the energy potential incorporating the surface effects. Using a variational approach, we construct the Euler-Lagrange equation together with the natural transition (jump) conditions. The surface effects are represented by an interface of a membrane type, with in-plane moduli different from those of either phase. The overall elastic behavior of the composite is characterized by five constants. Four of them, except the transverse shear modulus, are derived in simple closed forms using an approach of neutral inclusion. For the transverse shear, we derive the value based on the generalized self-consistent method.     

Thermo-elasto-plastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration

Functionally graded materials (FGMs) have recently been received with considerable interest, primarily as high temperature resistant materials for space vehicles subjected to high temperature environment. FGMs are one of the composite materials and consist of continuous change of composition of different material components from one surface to the other. FGMs usually fabricated at high temperature at which the FGMs have stress free condition. After the FGMs cooled from the fabrication temperature to the room temperature residual thermal stresses produced. In this paper, elasto-plastic thermal stresses in a rectangular plate (FGP) of a particle reinforced composite FGM are treated by finite element method due to the microscopic combination law when the FGP is subjected to three kinds of temperature conditions, first is cooling from the fabricated temperature to the room temperature, second is heating and last is heating after cooling from the fabricated temperature. In the analysis, the thermal stress constitutive equation of a particle-reinforced composite taking temperature change and damage process into consideration is used. The effects of the particle volume fraction and the three kinds of temperature conditions on the stresses in the matrix, stresses in the particle and macroscopic stress are discussed.     

Boundary element analysis of actual residual stresses in elastic plastic bodies under cyclic loading

The BEM was applied to the evaluation of an actual residual stress field in an elastic — perfectly plastic body subjected to any given cyclic loading. A new mechanical model describing this problem was used.

A corresponding discrete model based on both the direct and indirect versions of the BEM was proposed. The BEM approximation of stresses applied was similar to that one used in the elasto-plastic analysis in so called modified tractions and modified body forces algorithm. Some numerical tests have been carried out where BE solutions were compared with those obtained by means of the FE and FD methods. These comparisons show that the discrete model based on the BEM is efficient in the residual stress analysis.     

SEM in-situ investigation on failure of nanometallic film/substrate structures under three-point bending loading

Three-point bending tests on nanocrystalline Cu or Cu/Ni-film/Cu-substrate samples were conducted in-situ with scanning electron microscopy (SEM) observations. The SEM in-situ observations show undulation deformation of the surface of thin film, as the thin film fractures easily at the concave–convex points of deformation and multi-cracks appear on the surface of the thin film in a periodic fashion. The critical wavelength of undulation is calculated based on experimental observations, which are comparable with the theoretical predictions. For the Cu/Ni multi-layered films/substrate structures, the micro-cracking pattern depends on the interfacial strength between the film and the substrate, rather than the interfacial strength between the layers of films.