Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson’s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.     

Evolution of thermal stress in a coating/substrate system during the cooling process of fabrication

An analytical model is established for the thermal stress evolution in a film/substrate system during the cooling process of fabrication. Herein, heat transfer characteristics are incorporated which is critical for thermal spray coatings. The in situ temperature field solution is used to derive the instantaneous thermal stress field. Since the loss of thermal energy is account for, the new model may provide the basis for a more realistic prediction of the in situ thermal stress the fabrication process. The magnitude of thermal stress derived from the present model is lower than that of the classic one. The thermal stress is generated quickly and significantly during the initial seconds of the cooling process, and stabilizes later. The effects of several spray factors, such as the pre-heat temperature and the thicknesses of coating and substrate, are discussed and compared with a parallel experiment.     

On the matrix cracking stress and the redistribution of internal stresses in brittle-matrix composites

A concept is proposed to increase the matrix cracking stress of some brittle-matrix composites by taking advantage of the redistribution of internal stresses that occurs when a composite with phases that have dissimilar creep behavior is subjected to thermomechanical loading. The concept is elaborated through the stress analysis of a model unidirectional composite with constituents that exhibit linear viscoelastic behavior. It is shown that if a composite with a matrix that is less creep resistant than the fibers is subjected to a treatment involving both thermal and mechanical loading (e.g. creep test), stresses can be transferred from the matrix to the fibers, resulting in the stress–relaxation of the matrix. Furthermore, it is also shown that by the elastic recovery of the fibers, the matrix can be subjected to large compressive residual stresses at the end of the treatment. The conditions for the viability of this concept and the implications of fiber overloading and potential loss of composite-like behavior are discussed.     

Estimation of biaxial tensile and compression behavior of polypropylene using molecular dynamics simulation

The polymeric materials in general exhibit strong time–temperature dependence and viscoelastic behavior. The time–temperature superposition principle is typically used to estimate the long-term viscoelastic behavior. In addition, Mises criterion and Tresca criterion have been proposed to estimate the yield or failure stresses in a multiaxial stress state and Christensen failure criterion can be applied in the case of different tensile and compressive strengths. In this study, using molecular dynamics method, uniaxial and biaxial tensile and compression test simulations were performed for polypropylene at various strain rates and temperatures. It was observed that the compressive fracture stresses were higher than the tensile fracture stresses. In addition, the fracture stress was high at a low temperature and high strain rate and these fracture stresses are in good agreement with Christensen failure criterion curves. Furthermore, the long-term viscoelastic behavior can almost be predicted from the short-term viscoelastic behaviors at three different temperatures using time–temperature superposition principle. But, the simulations at a wide range of temperatures is important to predict the more accurate long-term viscoelastic behavior.     

Mechanisms of cracking and delamination within thick thermal barrier systems in aero-engines subject to calcium-magnesium-alumino-silicate (CMAS) penetration

An analysis has been conducted that characterizes the susceptibility to delamination of thermal barrier coated (TBC) hot-section aero-turbine components when penetrated by calcium-magnesium-alumino-silicate (CMAS). The assessment has been conducted on stationary components (especially shrouds) with relatively thick TBCs after removal from aero-engines. In those segments that experience the highest temperatures, the CMAS melts, penetrates to a depth about half the coating thickness, and infiltrates all open areas. Therein the TBC develops channel cracks and sub-surface delaminations, as well as spalls. Estimates of the residual stress gradients made on cross-sections (by using the Raman peak shift) indicate tension at the surface, becoming compressive below. By invoking mechanics relevant to the thermo-elastic stresses upon cooling, as well as the propagation of channel cracks and delaminations, a scenario has been presented that rationalizes these experimental findings. Self-consistent estimates of the stress and temperature gradients are presented as well as predictions of channel cracking and delamination upon cooling.     

Reliable stress and fracture mechanics analysis of complex components using a h–p version of FEM

We develop effective approaches with which complex three-dimensional components may be analysed with a high and virtually guaranteed accuracy. The main computational tool is a h-p version of FEM practically realized with the p-version program STRIPE having a mesh generator for automatic mesh refinement at edges and vertices. Use of advanced extraction methods and new theoretical approaches give exponential convergence rates for accuracies in all engineering data of interest. New methods for reliable calculation of local stresses and stress intensity data at edges and vertices to be used for fatigue dimensioning at fillets, damage tolerance assessment of three-dimensional flaws, etc., are given. A complex real-life problem is reliably analysed in order to demonstrate the practical usefulness of the procedures advocated. The technical details will be given in forthcoming papers.     

复合材料多尺度分析方法与典型元件拉伸损伤模拟

复合材料具有多尺度特性,多尺度模拟方法能够考虑细观损伤、演变对宏观材料性能和力学行为的影响,是复合材料响应分析的一种重要方法和手段。基于多尺度渐进展开理论,对复合材料弹性问题控制方程进行尺度分解,推导了细观尺度与宏观尺度的控制方程,建立了复合材料宏观和细观尺度响应之间的关联。基于协同多尺度计算策略,利用通用有限元软件的用户子程序与脚本二次开发,在宏观模型计算中实时调用细观模型进行多尺度渐进损伤模拟,实现了宏观和细观尺度的信息传递与反馈。建立的复合材料多尺度数值模拟方法可以快速集成细观损伤模型以及宏观唯象强度理论,具有良好的通用性。碳/碳复合材料拉伸模拟算例结果与试验结果吻合较好。     

Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading

The interlaminar stresses and displacements near the free-edges and ply cracks are investigated by using the state space equation method for general cross-ply laminates subjected to extension and/or thermal loading. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. Numerical solutions are compared with results obtained from other methods. It is found that the theory provides a satisfactory approximation to the stress singularity occurring in the vicinity of the free-edges and ply cracks.     

Stress-function variational method for stress analysis of bonded joints under mechanical and thermal loads

High interfacial stresses near the ends of adherends are responsible for debonding failure of bonded joints used extensively in structural engineering and microelectronics packaging. This paper proposes a stress-function variational method for determination of the interfacial stresses in a single-sided strap joint subjected to mechanical and thermal loads. During the process, two interfacial shear and normal (peeling) stress functions are introduced, and the planar stresses of adherends of the joints are expressed in terms of the stress functions according to the static equilibrium equations. Two coupled governing ordinary differential equations (ODEs) of the stress functions are obtained through minimizing the complementary strain energy of the joints and solved explicitly in terms of eigenfunctions. The stress field of the joints based on this method can satisfy all the traction boundary conditions (BCs), especially the shear-free condition near the adherend ends. Compared to results based on finite element method (FEM) and other analytic methods in the literature, the present variational method is capable of predicting highly accurate interfacial stresses. Dependencies of the interfacial stresses upon the adherend geometries, moduli and temperature are examined. Results gained in this study are applicable to scaling analysis of joint strength and examination of solutions given by other methods. The present formalism can be extended conveniently to mechanical and thermomechanical stress analysis of other bonded structures such as adhesively bonded joints, composite joints, and recently developed flexible electronics, among others.     

Study of thermal decomposition of methyl ethyl ketone peroxide using DSC and simulation

Methyl ethyl ketone peroxide (MEKPO) is a typical organic peroxide with thermally unstable nature that has been broadly employed in the manufacturing process of acrylic resins, as a hardening agent for fiberglass-reinforced plastics, and as a curing agent for unsaturated polyester resins. The aim of this study was to identify the characteristics of MEKPO 31 wt.% while mixing with contaminants, such as H(2)SO(4), HCl, and NaCl under runaway conditions. To acquire the thermal runaway data, DSC and a simulation were used for thermal analysis. The results showed that the thermal decomposition of MEKPO and MEKPO+H(2)SO(4) follows two stages. The first one can be modeled by using an empirical nth order rate equation. The second stage can be modeled as autocatalytic. MEKPO+HCl and MEKPO+NaCl included two independent autocatalytic reactions. The decomposition of MEKPO in the presence of Cl- ions (added in MEKPO either in the form of HCl or NaCl) follows a significantly different path, an earlier decomposition "onset" temperature, higher amount of generated thermal power and smaller temperature of no return (T(NR)) and time to maximum rate (TMR) values. Simulations based on experimental data indicated that the effect of H(2)SO(4) was the most dangerous contaminant on MEKPO 31 wt.%. However, the impact of Cl ions was also important. It is therefore recommended that the means of fire fighting employed for this substance to be free of Cl-.     

Modal analysis of carbon nanotubes and nanocones using FEM

Modal analysis of single-walled carbon nanotubes (SWCNTs) and nanocones (SWCNCs) was performed using a finite element method (FEM) with ANSYS. The vibrational behaviors of fixed beam and cantilever SWCNTs with different section types of a circle and an ellipse were modeled using three-dimensional elastic beams of carbon bonds and point masses. Also, the vibrational behaviors of fixed beam and cantilever SWCNCs with different disclination angles of 120°, 180°, and 240° were modeled using the same method. The beam element natural frequencies were calculated by considering the mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. Each mass element of the carbon atoms was assigned as a point mass at the nodes of the FEM elements. The natural frequencies of zigzag and armchair SWCNTs and SWCNCs were also computed. There were some differences between the findings obtained in this study and the molecular structural mechanics data available in the literature. The natural frequencies of SWCNCs were estimated depending on the geometrical type and disclination angle with different boundary conditions. The natural frequencies of the SWCNCs with disclination angles of 120°, 180°, and 240° increased significantly at higher modes of vibration.     

Simulation of the effect of material properties and interface roughness on the stress distribution in thermal barrier coatings using finite element method

A Finite Element Model (FEM) was developed to evaluate the stresses induced by the thermal cycling in a typical plasma-sprayed thermal barrier coating system (TBCs). The thermo-mechanical model of this multi-layer system takes into account the effects of thermal and mechanical properties, morphology of the top-coat/bond-coat interface and oxidation on the local stresses that are responsible for the micro-crack nucleation during cooling, especially near the metal/ceramic interface.Two top-coat/bond-coat geometries corresponding to different interfacial asperity morphologies (semicircle or sinusoidal) are modeled considering a two dimensional and periodic geometry. The effect of the geometry and the amplitude of asperities on stress distribution are examined to study the cause of the subsequent delamination of the TBCs system. Moreover, the effect of the creep in all layers and plastic deformation in the bond-coat as well as the oxidation in the perpendicular direction of the top-coat/bond-coat interface are examined toward the stress development and critical sites with respect to possible crack paths. In addition, crack initiation and propagation at the system was predicted.     

An effective method of stress intensity factor calculation for cracks emanating from a triangular or square hole under biaxial loads

This paper is concerned with stress intensity factors for cracks emanating from a triangular or square hole under biaxial loads by means of a new boundary element method. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfied and the crack‐tip displacement discontinuity elements proposed by the author. In the boundary element implementation, the left or the right crack‐tip displacement discontinuity element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called a Hybrid Displacement Discontinuity Method (HDDM). Numerical examples are included to show that the method is very efficient and accurate for calculating stress intensity factors for plane elastic crack problems. In addition, the present numerical results can reveal the effect of the biaxial loads on stress intensity factors.     

An investigation on thermal, metallurgical and mechanical states in weld cracking of Inconel 738LC superalloy

The influence of various conditions of Inconel 738 superalloy welding or deposition welding has been studied in order to shed light on the coupling between thermal, metallurgical and mechanical states in the heat affected zone (HAZ) in which cracking may occur particularly during welding and post-weld heat treatment. Predominant crack controlling factors have been highlighted thanks to different pre-weld and post-weld heat treatments, in addition to various welding rates and pre-heating prior to welding. These factors are mainly the material ductility related to the morphology and volume fraction of intermetallic precipitates and thermally induced residual stress. It has appeared that reducing thermally induced residual stress could be more effective for preventing cracking than controlling the material ductility in the related zones thanks to adjustment of pre-weld and post-weld heat treatments. With the objective of cracking remediation, welding on preheated parts leads to lower weld power, to reduce significantly thermal gradients, decreases thermally induced stress and impedes cracks formation despite some localized and temporary decrease in alloy ductility.     

Residual stress fields in surface-treated silicon carbide for space industry—comparison of biaxial and triaxial analysis using different X-ray methods

Any mechanical surface treatment and machining leaves ‘footprints’ in the form of residual stress fields in the surface region of technical parts or components, which are detectable by X-ray diffraction. In the present paper, we applied different X-ray methods to investigate the residual stress state in the near-surface zone of sintered silicon carbide after mechanical surface processing. Using the sin² ψ-based ‘universal plot’ method, we found steep gradients for the in-plane components σ₁₁ and σ₂₂ in the form of high compressive stresses at the surface, which change into tensile stresses within a few microns. To gain information on the triaxial residual stress state, we applied the scattering vector method, which is based on strain depth profiling by sample rotation around the diffraction vector. For the in-plane stresses, we observed gradients similar to those obtained by the ‘universal plot’ method, but they were shifted on the absolute scale towards tensile stress. We explain this difference by ‘pseudo-macroscopic’ tensile residual stress fields σ₃₃, which act normal to the surface and therefore pretend higher in-plane compressive stresses σ_ii (i = 1, 2), if they are not regarded in the evaluation procedure.     

Three-dimensional thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates using finite layer method

Finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates. Using this method, the 3D analysis is transformed into one dimensional analysis by virtue of the orthogonal properties of trigonometric interpolation functions. In the present study, the finite layer method is extended to the thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates, which may be combined with some symmetrical cross-plies. Full coupling between the thermal, electrical and mechanical fields is taken into consideration. Pre-buckling state is assumed to be steady, and initial thermal stresses are computed accordingly. The geometrical stiffness matrix is then formed, and the critical temperature and buckling mode are obtained. Numerical examples are presented to verify the proposed method. The critical temperature is determined for both the adiabatic and isothermal buckling processes. The thermal buckling behaviours of some piezoelectric laminates and the effects of the thermo-electro-mechanical coupling are investigated.     

冲击载荷下的齿轮动应力变化规律数值分析

基于虚拟制造方法建立了滚剃工艺的精确圆柱直齿轮三维几何模型,并进行线外啮合冲击动态仿真分析,得到了可靠的齿轮动应力变化规律。仿真结果表明：冲击加载时,不同工况下齿根两侧最大动应力的出现位置呈对称分布;冲击载荷下,齿根最大应力大于ISO标准静强度理论值,最大应力位置比ISO标准确定的最危险截面位置偏高;冲击载荷峰值相同时,冲击时间越短,产生的动应力越大。     

Simulations of fracture and fragmentation of geologic materials using combined FEM/DEM analysis

Results are presented from a study investigating the effect of explosive and impact loading on geological media using the Livermore distinct element code (LDEC). LDEC was initially developed to simulate tunnels and other structures in jointed rock masses with large numbers of intact polyhedral blocks. However, underground structures in jointed rock subjected to explosive loading can fail due to both rock motion along preexisting interfaces and fracture of the intact rock mass itself. Many geophysical applications, such as projectile penetration into rock, concrete targets, and boulder fields, require a combination of continuum and discrete methods in order to predict the formation and interaction of the fragments produced. In an effort to model these types of problems, we have implemented Cosserat point theory and cohesive element formulations into the current version of LDEC, thereby allowing for dynamic fracture and combined finite element/discrete element simulations. Results of a large-scale LLNL simulation of an explosive shock wave impacting an elaborate underground facility are also discussed. It is confirmed that persistent joints lead to an underestimation of the impact energy needed to fill the tunnel systems with rubble. Non-persistent joint patterns, which are typical of real geologies, inhibit shear within the surrounding rock mass and significantly increase the load required to collapse a tunnel.     

Analysis of multi-layered filament-wound composite pipes under combined internal pressure and thermomechanical loading with thermal variations

The composite pipes manufactured by filament winding technology have anisotropic behavior owing to different reinforced ply angles. Composite pipes can be exposed to the thermomechanical loading due to hot fluid that flows into them. In this paper, based on the three-dimensional anisotropic elasticity, an exact elastic solution for thermal stresses and deformations of the pipes under internal pressure and a temperature gradient has been studied. Giving heat convection conditions the variation of temperature field within the pipe is obtained by solving the conduction equation at the wall. The influence of temperature field in the governing equations of thermoelasticity has been considered via a constitutive law. The shear extension coupling is also considered because of lay-up angles. Stress, strain and deformation distributions for different angle-ply pipe designs are investigated using the present theory.     

A solution method for frictional contact problems of a crack in FGMs under mechanical and thermal loads

This article provides a numerical treatment of a finite crack in an interfacial layer with spatially varying elastic properties under in-plane mechanical and thermal loading conditions. The variation of stress intensity factors and energy release rates with the functions which are governing the material properties of the interfacial layer is studied. Transient and steady-state response of a central crack in FGMs subjected to the mechanical and thermal loads are investigated. Unlike earlier studies which consider the cracks encountered as open, the current investigation studies cracks in an essentially compressive environment in which the crack faces are in contact and frictional effects play an important role. To solve this contact problem, a simple and efficient, iterative finite element method developed by authors is used. Numerical examples are provided to verify the technique and the results are compared with those of the published papers. This revised version was published online in July 2006 with corrections to the Cover Date.