Maximum Stress Failure Criterion Research Articles

Optimization of hybrid laminated composites using a genetic algorithm

This work aims at developing a genetic algorithm (GA) to pursue the optimization of hybrid laminated composite structures. Fiber orientation (predefined ply angles), material (glass-epoxy or carbon-epoxy layer) and total number of plies are considered as design variables. The GA is chosen as an optimization tool because of its ability to deal with non-convex, multimodal and discrete optimization problems, of which the design of laminated composites is an example. First, the developed algorithm is detailed explained and validated by comparing its results to other obtained from the literature. The results of this study show that the developed algorithm converges faster. Then, the maximum stress, Tsai-Wu and Puck (PFC) failure criteria are used as constraint in the optimization process and the results yielded by them are compared and discussed. It was found that each failure criterion yielded a different optimal design.

Drop-weight impact tests and finite element modeling of cast acrylic plates

Low-velocity impact tests on cast acrylic (PMMA) plates were conducted using an instrumented drop-weight impact machine under various temperatures. Radial cracks were induced and the impact force histories were recorded. Results indicated that there was a glass transition temperature of cast acrylic between 185 and 200 °F. Ultrasonic assessments on the impacted acrylic plates were then performed using different transducers. Focused transducers provided more accurate results than flat ones. In addition, the higher the ultrasound frequency, the better the resolution. Finally, the drop-weight impact responses were simulated using LS-DYNA. Two node-splitting techniques, sudden releasing and stepwise releasing, based on maximum tensile stress failure criterion, were implemented for this study. The maximum tensile stress failure criterion was adopted to capture the onset of crack initiation and crack propagation. The node release methods enabled us to calculate the strain energy release rates of cast acrylic. Numerical simulations were compared with experimental results and good agreements were achieved.

MULTISCALE PROGRESSIVE FAILURE ANALYSIS OF PLAIN-WOVEN COMPOSITE MATERIALS

The paper presents an overview of multiscale modeling of advanced fibrous composite materials. Following the review, a nonlinear, fully three-dimensional, numerical model is proposed which is suitable for multiscale elastic and progressive failure analysis of plain-woven composite materials. The proposed model is developed for implementation into the Finite Element code ABAQUS/Explicit as a user-defined subroutine for constant stress (one integration point) solid elements. The multiscale strategy applied in this paper uses a closed-form solution approach for homogenization of the mesoscale properties of a woven composite. A mosaic model of the woven composite's Representative Volume Element (RVE) is used for deriving the micromechanical relations used for homogenization. The composite RVE model used herein is composed of UD interlacing yarns (fill and warp yarns) and matrix-rich regions. For failure and damage analysis, the following features are implemented in this work: material nonlinearity for pure in-plane shear deformation; physically-based failure criteria for matrix failure in the UD yarns; maximum stress failure criteria for failure of fibers in the UD yarns and of the pure matrix in the resin-rich regions and energy-based damage mechanics. The proposed strategy, which has been implemented and tested for a special case of an in-plane damage, has some evident advantages compared to the other approaches, especially for application to full-scale simulations, i.e., component and structural scales. A comparison of the proposed model with experimental data shows a good correlation can be achieved.

Quantum behaved Particle Swarm Optimization (QPSO) for multi-objective design optimization of composite structures

We present a new, generic method/model for multi-objective design optimization of laminated composite components using a novel multi-objective optimization algorithm developed on the basis of the Quantum behaved Particle Swarm Optimization (QPSO) paradigm. QPSO is a co-variant of the popular Particle Swarm Optimization (PSO) and has been developed and implemented successfully for the multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are – the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria; Failure Mechanism based Failure criteria, Maximum stress failure criteria and the Tsai–Wu Failure criteria. The optimization method is validated for a number of different loading configurations – uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences as well as fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented. Also, the performance of QPSO is compared with the conventional PSO.

Hierarchical Evaluation of Failure Parameters in Composite Plates

This paper presents a failure analysis of simply supported, orthotopic plates subjected to global/local bending loadings via the Navier-type solution. Carrera's unified formulation is adopted in order to implement a large variety of two-dimensional theories. The minimum first-ply failure loading and the failure locations are obtained via classical, refined, zig-zag, layerwise, and mixed theories. The maximum stress, Tsai-Wu, Tsai-Hill, Hoffman, and Hashin failure criteria are assumed. The accuracy of two-dimensional theories is assessed via comparison with the three-dimensional Pagano's solution, which has here been extended to the considered cases. The influence of the side-to-thickness ratio, the aspect ratio, the material properties, the lamination layup, and the loading localization is investigated. A hierarchy among the Carrera's unified formulation two-dimensional models has been established.

Applying the sequential neural-network approximation and orthogonal array algorithm to optimize the axial-flow cooling system for rapid thermal processes

The sequential neural-network approximation and orthogonal array (SNAOA) were used to shorten the cooling time for the rapid cooling process such that the normalized maximum resolved stress in silicon wafer was always below one in this study. An orthogonal array was first conducted to obtain the initial solution set. The initial solution set was treated as the initial training sample. Next, a back-propagation sequential neural network was trained to simulate the feasible domain to obtain the optimal parameter setting. The size of the training sample was greatly reduced due to the use of the orthogonal array. In addition, a restart strategy was also incorporated into the SNAOA so that the searching process may have a better opportunity to reach a near global optimum. In this work, we considered three different cooling control schemes during the rapid thermal process: (1) downward axial gas flow cooling scheme; (2) upward axial gas flow cooling scheme; (3) dual axial gas flow cooling scheme. Based on the maximum shear stress failure criterion, the other control factors such as flow rate, inlet diameter, outlet width, chamber height and chamber diameter were also examined with respect to cooling time. The results showed that the cooling time could be significantly reduced using the SNAOA approach.

Modelling of chip separation in machining unidirectional FRP composites by stiffness degradation concept

Progressive failure of unidirectional glass fiber-reinforced polymer composites (FRP) was studied using finite element analysis in orthogonal machining. Chip formation process and damage modes such as matrix cracking, fiber–matrix debonding and fiber breaking were modelled by degrading the material properties. Damage analysis was carried out using Hashin, Maximum stress and Hoffman failure criteria. After damage was detected, selective stiffness degradation was applied to the workpiece material. The objective of this study is to better understand the chip formation process and to analyse the cutting-induced damage from initiation stage until complete chip formation. The effect of the fiber orientation on cutting forces and sub-surface damage was investigated with different failure criteria. The results were addressed in terms of cutting forces evolution and damage progression in the composite structure during machining. It was demonstrated that the use of the stiffness degradation concept with the appropriate failure criterion responds potentially in a predictable fashion to changes in chip formation process for machining of FRPs.

Investigation on short-term burst pressure of plastic pipes reinforced by cross helically wound steel wires

Plastic pipes reinforced by cross helically wound steel wires (PSP), which have exhibited excellent mechanical performance, consist of inner polyethylene (PE) layer, winding layer and outer PE layer. The winding layer is composed of two monolayers where steel wires are cross helically wound. An analytical procedure is developed to predict the short-term burst pressure of PSP as the monolayer is assumed to be elastic and orthotropic. The 3D anisotropic elasticity and Maximum Stress Failure Criterion are employed in the formulation of the elasticity problem. Good agreement between the theoretical results and the experimental data shows that the proposed approach can well predict the short-term burst pressure of PSP.

Artificial immune system for multi-objective design optimization of composite structures

We present a new, generic method/model for multi-objective design optimization of laminated composite components using a novel multi-objective optimization algorithm developed on the basis of the artificial immune system (AIS) paradigm. A co-variant of the popular clonal selection principle called as the Objective Switching Clonal Selection Algorithm (OSCSA) has been developed and implemented successfully for the multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are—the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria; failure-mechanism-based failure criteria, maximum stress failure criteria and the Tsai-Wu failure criteria. The optimization method is validated for a number of different loading configurations—uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences as well as fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented.

An Initial and Progressive Failure Analysis for Cryogenic Composite Fuel Tank Design

Thermal residual stresses, internal pressure stresses, and acceleration stresses during launch were evaluated and quantified for cryogenic composite fuel tank design. Both failure initiation and progression of graphite/epoxy laminate system (IM7/977-2) [0/90/90/0/0/90]s and graphite/BMI laminate system (IM7/5250-4) [0/90/90/0/0/90]s were investigated using the non-isothermal classical laminate and plate theory (CLPT) and the maximum stress failure criterion. The thermal residual stresses in the transverse direction are the dominant stresses on each ply in the launch stage. After initial ply cracking, through-the-thickness temperature change of a laminate related to fuel leakage as well as a laminate stiffness matrix change was applied to the progressive failure analysis. The fuel leakage-based progressive analysis shows a higher number of initial ply cracking does not necessarily mean a higher chance of matrix cracking in all plies. The graphite/BMI laminate has such an advantage as transverse thermo-mechanical resistance over the graphite/epoxy laminate at an initial exposure to —253°C and 1500 kPa. In terms of complete laminate matrix cracking, however, the graphite/ epoxy laminate is more resistant to transferring stresses to other plies than the graphite/BMI laminate.

Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures

We present a generic method/model for multi-objective design optimization of laminated composite components, based on vector evaluated particle swarm optimization (VEPSO) algorithm. VEPSO is a novel, co-evolutionary multi-objective variant of the popular particle swarm optimization algorithm (PSO). In the current work a modified version of VEPSO algorithm for discrete variables has been developed and implemented successfully for the, multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are – the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria; failure mechanism based failure criteria, Maximum stress failure criteria and the Tsai–Wu failure criteria. The optimization method is validated for a number of different loading configurations – uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences, as well fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented.

Design optimization of composites using genetic algorithms and failure mechanism based failure criterion

In this paper, minimum weight design of composite laminates is presented using the failure mechanism based (FMB), maximum stress and Tsai–Wu failure criteria. The objective is to demonstrate the effectiveness of the newly proposed FMB failure criterion (FMBFC) in composite design. The FMBFC considers different failure mechanisms such as fiber breaks, matrix cracks, fiber compressive failure, and matrix crushing which are relevant for different loading conditions. A genetic algorithm is used for the optimization study. The Tsai–Wu failure criterion over predicts the weight of the laminate by up to 86% in the third quadrant of the failure envelope compared to FMB and maximum stress failure criteria, when the laminate is subjected to compressive–compressive loading. It is found that the FMB and maximum stress failure criteria give comparable weight estimates. The FMBFC can be considered for use in the strength design of composite structures.

A thermo-viscoelastic analysis of process-induced residual stress in fibre-reinforced polymer–matrix composites

Process-induced residual stress in fibre-reinforced thermoset polymer–matrix composites was analysed using a thermo-viscoelastic micromechanical model and the finite element method. A three-dimensional unit cell with glass fibre and epoxy polymer–matrix, representing the periodic microstructure of unidirectional fibre-reinforced composites, was considered to compute cure residual stress of fibre composites induced by chemical shrinkage of the epoxy resin and thermal cooling contraction of the whole fibre and resin system. The constitutive behaviour of the epoxy matrix was described by a cure and temperature-dependent viscoelastic material model. Compared to an elasticity solution, a reduction in residual stress was predicted due to the stress-relaxation caused by the viscoelastic behaviour of the epoxy matrix. Calculated residual stress shows strong dependency on the fibre volume fraction and fibre packing. After the cure process is complete, residual stress tends to relax to a constant value. The effect of residual stress on damage and failure of the model was also studied using the maximum stress failure criterion combined with a post-failure stiffness reduction technique. Damage onset, in terms of the location and the load level, was shown to be clearly influenced by the residual stress for both normal and shear loading. Initial and final failure envelopes, predicted for biaxial normal (longitudinal and transverse) loading and combined shear (longitudinal) and normal (transverse) loading, were shown to be shifted and contracted by the inclusion of residual stress. For final failure, residual stress was seen to have little effect on the load levels for longitudinal failure but greatly affected the load levels for transverse and shear failure. Residual stress could be detrimental or beneficial depending on the state of existing residual stress and the loading conditions.

Analysis of bolted joints in composite laminates: Strains and bearing stiffness predictions

Abstract A review of the investigations conducted on mechanically fastened joints is presented. A finite-element model is developed to predict the response of pin-loaded composite plates. The model takes into account contact at the pin–hole interface, progressive damage, large deformation theory, and a nonlinear shear stress–strain relationship. To predict progressive ply failure, four different analyses combining Hashin and the maximum stress failure criteria, and different associated degradation rules are conducted. The objectives of the study are to determine the influence of the failure criteria and the associated degradation rules on the predictions of the strains around the hole and the bearing stiffness. Predictions are compared with experimental results. It appears that agreement between the two depends on an appropriate selection of the failure criterion and the degradation rule. Better agreement between experimental results and numerical predictions is observed with the maximum stress criterion.

Quasi-non-linear fracture mechanics analysis of the double cantilever beam specimen

A quasi-non-linear fracture mechanics model based on beam on elastic foundation theory is applied for analysis of the double cantilever beam (DCB) specimen for determination of fracture energy of wood. The properties of the elastic foundation are chosen so that the perpendicular-to-grain tensile strength and fracture energy properties of the wood are correctly represented. It is shown that this particular choice of foundation stiffness makes a conventional maximum stress failure criterion lead to the same solution as the fracture mechanics compliance method. Results of linear elastic fracture mechanics are obtained as a special case by assuming an infinitely large value of the perpendicular-to-grain tensile strength. The quasi-non-linear fracture mechanics model is compared with other models and with results of tests conducted to reveal the influence of the geometrical properties of the DCB specimen. In addition, the appropriateness of choice of the foundation stiffness is investigated.

Quasi-non-linear fracture mechanics analysis of the splitting failure of single dowel joints loaded perpendicular to grain

A quasi-non-linear fracture mechanics model based on beam on elastic foundation theory is applied for analysis of dowel joints with a single dowel loaded perpendicular to grain. The properties of the elastic foundation are chosen so that the perpendicular-to-grain tensile strength and fracture energy properties of the wood are correctly represented. It is shown that this particular choice of foundation stiffness makes a conventional maximum stress failure criterion lead to the same solution as the compliance method of fracture mechanics. Results of linear elastic fracture mechanics are obtained as a special case by assuming an infinitely large value of the foundation stiffness. Results of tests on so-called plate joints are compared with theoretical predictions, showing good agreement for variations in initial crack length as well as edge distance.

Finite element modelling of damage progression in non-crimp fabric reinforced composites

Progressive failure of non-crimp fabric composite laminate was studied using finite element analysis with stress-based failure criteria. The laminate was loaded in tension and has the lay-up of [0/90] s with both in-phase and out-of-phase placed transverse-tow layers considered. The finite element model was created from a cross-section Representative Volume Element of the laminate. Damage analysis was first carried out using the Maximum Stress failure criterion. After damage was detected within the laminate, point-wise selective stiffness degradation was applied to the model through a user-defined material subroutine. For the material under study, it has been shown that damage initially occurs in either the transverse tows or the resin pockets, and gradually spreads across the transverse tows and resin pockets. As the load reaches a critical point, damage finally progresses into the longitudinal tows and causes laminate failure very quickly. Stages of damage evolution, from initiation until final failure, are reflected in the knee behaviour of the overall load–strain trace. Studies show that tow shape plays a role in the failure progress, especially the load levels for initial and final failure. Analyses using different combinations of failure criteria for the tows and resin pockets were performed and the results were addressed in terms of the location of initial damage and the load levels of initial damage and final failure.

A Finite Element Investigation on Progressive Failure Analysis of Composite Bolted Joints Under Thermal Environment

The progressive failure analysis of composite bolted joints under thermal environment has been investigated using the finite element method. The emphasis has been on the computational aspects of the problem. The ultimate failure loads and pin-bearing stresses have been computed using different failure criteria and the results have been compared with the experimental data as published in the open literature. In reality, bolted joints have been employed to various situations where the amount of load to be transferred is relatively high and on many occasions thermal effect is an important consideration. So the effect of material property degradation due to temperature has also been considered in this investigation. Progressive damage analyses have been performed for different laminates to give complete load-deflection path beyond failure load that will serve as a future reference. The pin has been modeled as a rigid object and load has been imparted on the structure as a displacement-controlled process to simulate the experimental situation in the laboratory environment. Contact between the bolt and the laminate has been considered in the analysis. A number of “User Subroutines” for ABAQUS software have been developed to incorporate Hashin, maximum stress, and Tsai-Wu failure criteria in the analysis. The effectiveness and performance of various well-known failure criteria as mentioned above have been evaluated and the results have been presented in graphical form.

Predicting the ultimate load of a CFRP wingbox

Abstract The finite element method in conjunction with the Soutis–Fleck model is used to predict the residual strength after impact of a carbon-fibre reinforced plastic wingbox subjected to a cantilever type loading. The maximum stress failure criterion further validates the Soutis–Fleck model predictions. The Soutis–Fleck model predicts that the wingbox fails at a tip load of 99.2 kN, approximately 5.5% less than the experimental observation.

The Effect of Lamps Radius on Thermal Stresses for Rapid Thermal Processing System

The concept of rapid thermal processing has many potential applications in microelectronics manufacturing, but the details of chamber design remains an active area of research. In this work the influence of lamps radius on the thermal stresses in a wafer during the cooling process is studied in detail. Since the equations governing the present thermal-elastic system are coupled in nature, the solution for the temperature and stresses must proceed simultaneously by using a fully implicit finite difference method. After the thermal stresses are obtained, the optimum lamps radii for various heights of the chamber under the constant power ramp-down control scheme are determined based on the maximum shear stress failure criterion. The shortest cooling time that can significantly reduce the thermal budget and dopant redistribution is also predicted by applying the maximum stress control scheme. The result obtained is useful in the design of a reliable rapid thermal processor based on a more practical consideration, thermal stress.