Maximum Principal Stress Criterion Research Articles

Dual boundary element analysis of fatigue crack growth, interaction and linkup

Multiple-site and widespread fatigue damage have been an issue to the aircraft and construction industry for a long period. Structural components develop cracks at several locations which grow with crack paths that are difficult to predict. When two cracks approach one another, their stress fields influence each other leading to an enhancing or shielding effect which depends on the position and orientation of the cracks. Since there are no generalized analytical methods for predicting crack stress fields, simulation of multiple-crack growth is an important and challenging task which is still an evolving area of research.This paper describes a two-dimensional application of the dual boundary element method (DBEM) to the analysis of mixed-mode multiple-crack growth in linear elastic fracture mechanics, under fatigue loading. The crack-growth process is simulated with an incremental multiple-crack extension analysis based on the maximum principal stress criterion. For each increment of the analysis, in which crack extensions are modelled with new straight boundary elements, the DBEM is applied to perform a single-region stress analysis of the cracked structure and the J-integral is used to compute the stress intensity factors. The incremental analysis is based on a prediction–correction technique that defines, in each increment of the analysis, the direction and the extension of the multiple interacting cracks, thus taking into account the discreteness of the analysis and ensuring that the requirement of the path uniqueness is satisfied. Based on the ligament yield criterion which assumes that when the plastic zones of two adjacent cracks touch each other, the ligament between the cracks fails and the cracks coalesce, plates with multiple-site damage can be analysed. The fatigue life and residual strength of the structure are introduced as a post-processing procedure on the results of the multiple-crack growth. Results of this incremental analysis are presented for several geometries with multiple-site damage, demonstrating the accuracy and efficiency of the strategies adopted in the analysis.

Modeling of fracture in small punch tests for small- and large-scale yielding conditions at various temperatures

We present a systematic numerical study on temperature dependent fracture mode change in small punch tests. Following Needleman and Tvergaard (2000), we model the material as thermo-inelastic, where the ductile fracture mode, by void nucleation, growth and coalescence is accounted for by Gurson׳s porous metal plasticity (Gurson, 1977). The brittle fracture mode by cleavage is accounted for by Ritchie–Knott–Rice׳s deterministic maximum principal stress criterion (Ritchie et al., 1973). The well-known problem of mesh dependence associated with softening material behavior is remedied by using an integral type nonlocal formulation similar to that presented in Tvergaard and Needleman (1995). Two length scales are incorporated into the constitutive relations: the ductile fracture length scale is based on the average inclusion distance and associated with the nonlocal evolution equation for the porosity. The brittle fracture length scale is based on the average grain size and associated with the material region at which the maximum principal stress is averaged out. The material model is used to simulate small punch tests at −196°C, −158°C and 25°C of notched and unnotched specimens of P91 steel representative for small- and large-scale yielding conditions, respectively. The simulated fracture modes and patterns show a very good agreement with experiments: for −196°C brittle fracture propagating normal to the maximum (tensile) principal stress prevails. For 25°C ductile fracture is governed by shear localization with voidage. The simulations also show that the deformation energy is considerably higher for the upper shelf tests compared to the lower shelf tests.

The Influence of Particle Shapes on Strength and Damage Properties of Metal Matrix Composites.

The influence of the distribution of particle shapes, locations and orientations on the mechanical behavior of the particle reinforced Metal-Matrix Composite (MMC) is studied through finite element (FE) method under different loading conditions in this investigation. The FE-model with multi-particle is generated through the random sequential adsorption algorithm, with the particles treated respectively as elastic-brittle circular, regular octagon and hexagon and square shape. Ductile failure in metal matrix, brittle fracture of particles and interface debonding are taken into account during the simulations. 2D cohesive element is applied to simulate the debonding behavior of interface. The damage models based on the stress triaxial indicator and maximum principal stress criterion are developed to simulate the ductile failure of metal matrix and brittle cracking of particles, respectively. Simulation results show that the interface debonding dominates the failure process under the loading, while the damage in particle grows at slowest rate compared with those in matrix and interface.

Dynamic modeling of Kevlar KM2 single fiber subjected to transverse impact

In this paper, the transverse impact onto a Kevlar KM2 single fiber is studied using analytical and numerical models. The impact response of fibers with reduced longitudinal shear moduli (‘string’ model) is studied with a 3D finite element model and the wave propagation results converge to the classic 1D analytic solution that supports only axial loads. A dispersive flexural wave mode is predicted numerically for the single fiber during transverse impact due to its finite longitudinal shear modulus. The numerical results are confirmed with an analytical solution derived for the response of an infinitely long Euler–Bernoulli beam subjected to a constant velocity impact. Fiber bounce is predicted for impact with a cylindrical projectile with fiber velocity exceeding impact velocity by 60–80%. At short time scales significant transverse compressive stresses and strains develop in the fiber and the magnitude depends on the impact velocity. The breaking speed predicted by the 3D model based on maximum principal stress criterion for a single fiber is between 26% (membrane failure) and 76% (combined membrane and flexure failure) less than the 1D analytical solution. The flexural wave and projectile fiber interactions induce curvatures in the fiber significant enough to induce compressive fiber failure and fibrillation.

Multi-axial brittle failure criterion using Weibull stress for open Kelvin cell foams

Foam structures have found an increasingly wide utilization in modern industry because of their porous geometric characteristic and favorable mechanical properties like lightness, high strength and so on. Elastic buckling, plastic yielding, brittle fracture and crushing are typical failure mechanisms of foam structures. The influences of foam geometry and morphology on the failure mechanisms are still not fully understand. In this paper the Kelvin cell model is used to simulate the foam structure and to study the influence of relative density and geometric properties on failure behavior. By extensive FEM analyses of representative volume elements under multi-axial loading with periodic boundary conditions the macroscopic failure limit surface is calculated in stress space. Locally at the microstructure the probabilistic Weibull model and the maximum principal stress criterion are used as failure criterion.

Micromechanical Analysis of SiC/Al Metal Matrix Composites: Finite Element Modeling and Damage Simulation

The influence of interface strengths and microstructures on the strength and damage of SiC particle reinforced aluminum Metal Matrix Composite (MMC) is investigated under uniaxial tensile, simple shear, biaxial tensile and combined tensile and shear loadings. An algorithm to generate automatically the microstructural models of MMCs with random distribution of particle shapes, dimensions, orientations and locations is proposed and implemented within Matlab. A damage model based on the stress triaxial indicator is developed to simulate the ductile failure of metal matrix, the other damage model based on the maximum principal stress criterion is developed to simulate the brittle failure of SiC particles, and 2D cohesive element is utilized to describe interface decohesion between matrix and particles. A series of numerical experiments are performed to study the macroscopic stress–strain relationships and microscale damage evolution in MMCs under different loading conditions.

Strength Analysis of Syntactic Foams Using a Three-Dimensional Continuum Damage Finite Element Model

The failure behavior of the syntactic foams is investigated based on a three-dimensional (3D) micromechanical finite element (FE) model, by varying the volume fraction, the wall thickness of the hollow particles, and the interfacial strength. The maximum principal stress criterion is adopted to determine the state (damaged or undamaged) for both interface and matrix. Material property degradation is used to describe the mechanical behavior of those damaged elements. The current model can reasonably predict the tensile strength of the syntactic foams with high volume fractions (40%–60%). The failure mechanism of the syntactic foam under uniaxial tension is captured by analyzing the stress–strain curves and the contours of damaging evolution process. Results from the quantitative simulations demonstrate that the tensile strength of the syntactic foam can be improved effectively by enhancing the interfacial strength.

English

The aim of this study was to analyze the biomechanical behavior of lower premolars regarding the non-carious cervical lesion (NCCL) depth, load type and restoration status, using finite element analysis. Two-dimensional virtual model simulating a healthy lower premolar were created using the CAD software. Based on this image, five models were generated: healthy (H), three types of NCCLs: small lesion (SL – 0.5 mm deep), medium lesion (ML – 1.0 mm), deep lesion (DL – 1.5 mm), and restored lesion (RL). The models were export to a CAE software (ANSYS Finite Element Analysis Software), the areas of all structures were plotted and each model was meshed using a control mesh device. All of the virtual models were subjected to two occlusal load types, (100N each): occlusal load (OL) and buccal load (BL) on buccal cusp. The magnitude and the stress distribution were obtained using the von Mises and maximum principal stress criteria (σ1), in MPa. The quantitative analysis of stress (MPa) was identified at three points of the NCCLs: enamel surface on its upper wall , dentin at the bottom wall and dentin on the lower wall. The results showed a direct relation between sequential removal of cervical structure and higher stress concentration for any groups and for both loads types. For OL the highest value of stress was 8.8 MPa for DL on upper wall of NCCLs.The BL exhibited higher stress values in comparison to the OL for all models.In addtion, the BL was responsible for providing the highest stress accumulation on the bottom wall, 38.2 MPa for DL. The restoration with composite resin was able to restore a stress distribution close to the healthy model, for both load types. In conclusion, the extent of non-carious cervical lesion and loading conditions influenced the stress distribution pattern of lower premolar. The outer load seems to be more critical in affecting the biomechanical behavior of lower premolars, regardless of the lesion size . The restoration of NCCLs with composite resin appears to recover the biomechanical behavior, similar to healthy model.

A Finite Element Simulation for Orthogonal Cutting of UD-CFRP Incorporating a Novel Fibre-matrix Interface Model

The rapid increase in industrial utilisation of carbon fibre reinforced plastic (CFRP) composites in recent years has led to growing interest in numerical modelling of material behaviour and defect formation when machining CFRP. The inhomogeneous/anisotropic nature of CFRP however presents considerable challenges in accurately modelling workpiece defects such as debonding between the matrix and fibre phase following cutting operations. Much of the published literature has involved the use of zero thickness cohesive elements to represent the fibre-matrix interface, despite the inability of such elements to model compressive stresses. This paper details a new approach for characterising the interface region in a two-dimensional explicit finite element simulation when orthogonal machining unidirectional (UD) CFRP laminates. A cohesive zone model based on a traction-separation law is applied to small thickness (0.25μm) interface elements in order to accommodate compressive failure, which is implemented via a bespoke user subroutine. Fibre fracture is based on a maximum principal stress criterion while elastic-plastic behaviour to failure is used to represent matrix damage. The influence of varying fibre orientations (45°, 90°, 135°) on predicted cutting and thrust forces were validated against published experimental data. While the former was generally within 5% of experimental data for workpieces with 90° and 135° fibre directions, predicted thrust forces were typically underestimated by ∼30-60%. The corresponding chip formation mechanisms and sub-surface damage due to the different material phases were also investigated. The proposed model was able to predict composite behaviour and defect formation that was comparable to experimental high speed camera images outlined in the literature.

Failure mechanism of PMI foam core sandwich beam in bending

Polymethacrylimide (PMI) foams have been widely applied in aerospace engineering as the core material of sandwich structures. This paper proposes a modified model to predict the constitutive relation of PMI foams and compares it to existing testing data. The study is then applied to the investigation of the failure mechanism of PMI foam core sandwich beams in bending. Corresponding bending tests were carried out where a complex failure process was observed through a high-speed camera. Numerical model of the foregoing sandwich beam is developed, in which the maximum principal stress criteria is used to predict damage propagation in PMI foam core. Both results from tests and numerical simulation validate the reliability of the theoretical prediction of the failure of PMI foam core sandwich beam using the proposed modified model of PMI foams. This study provides a theoretic tool for the design of sandwich structures with PMI foam core.

Numerical Study on Crack Propagation by Using Softening Model under Blasting

A mixed failure criterion, which combined the modified maximum principal stress criterion with the damage model of tensile crack softening, was developed to simulate crack propagation of rock under blasting loads. In order to validate the proposed model, a set of blasting models with a crack and a borehole with different incident angles with the crack were established. By using this model, the property of crack propagation was investigated. The linear equation of state (EOS) was used for rock, and the JWL EOS was applied to the explosive. In order to validate the numerical simulation results, experiments by using PMMA (polymethyl methacrylate) with a crack and a borehole were carried out. The charge structure and incident angle of the blasting experimental model were the same as those in the numerical models. The experiment results agree with the numerical simulation results.

Mechanical weakening of devitalized teeth: three-dimensional Finite Element Analysis and prediction of tooth fracture.

To determine to which extent cavity preparation and each step of dentine removal in the process of root canal treatment (access cavity preparation and root canal enlargement) both individually and jointly contribute to the weakening of the tooth. Numerical analysis using finite element method (FEM) of separate and combined influence of two-surface Class II preparation and root canal treatment was undertaken to evaluate the decrease in tooth strength. The influence of the two stages in root canal treatment, access cavity preparation and root canal enlargement, was also analysed separately and jointly. After each of these phases, the crown was restored with composite resin, and the FEA was performed only on restored teeth. To estimate the influence of all these procedures on tooth fracture resistance numerically, a Failure Index based on the maximum principal stress criterion (MPCS) was applied. Compressive and tensile stresses were analysed separately and corresponding Failure Indices were calculated. A two-surface resin composite restoration weakened the tooth by 23.25%. Nevertheless, the Failure Indices showed that this tooth was not likely to fracture even under high occlusal stress (710N). However, after access cavity preparation, the Failure Indices reached the point where, under high occlusal force that may occur in the posterior area, a tooth fracture occurred. The enlargement of root canals had an additional, but relatively small impact on tooth weakening, making the tooth even more susceptible to fracture. The combined influence of both cavity preparation and root canal enlargement led to weakening of 62.6% under a load of 710N, ultimately causing tooth fracture. The combined finite element method and the maximum principal stress analysis gave insight into the fracture mechanisms of teeth with two-surface composite restorations followed by root canal preparation. Removal of tooth tissue, despite its subsequent restoration with dental materials, weakened the tooth by changing the stress intensity and distribution through tooth structures. Access cavity preparation had the greatest influence on tooth strength whilst canal enlargement did not contribute to this process substantially.

Finite Element Analysis of the Microstructure–Strength Relationships of Metal Matrix Composites

The influence of the shape and spatial distribution of reinforced particles on strength and damage of metal matrix composite (MMC) is investigated through finite element method under uniaxial tensile, simple shear, biaxial tensile, as well as combined tensile/shear loadings. The particle shapes change randomly from circular to regular n-sided polygon (3 ≤ n ≤ 10); the particle alignments are determined through a sequentially random number stream and the particle locations are defined through the random sequential adsorption algorithm. The ductile failure in metal matrix and brittle failure in particles are described through damage models based on the stress triaxial indicator and maximum principal stress criterion, respectively, while the debonding behavior of interface between particles and matrix is simulated through cohesive elements. The simulation results show that, under different loadings, interface debonding is the dominated failure mechanism in MMCs and plastic deformation and ductile failure of matrix also play very important roles on the failure of MMCs.

Micromechanical study of influence of interface strength on mechanical properties of metal matrix composites under uniaxial and biaxial tensile loadings

The influence of particle arrangements and interface strengths on the mechanical behavior of the particle reinforced metal–matrix composite (MMC) is investigated under different loading conditions in this work. During the loading process, three different failure mechanisms are distinguished in MMC: ductile failure in metal matrix, brittle failure in SiC particles and interface debonding between matrix and particles. The damage models based on the stress triaxial indicator and maximum principal stress criterion are developed to simulate the failure process of metal matrix and SiC particles. Meanwhile, 2D cohesive element is utilized to describe the debonding behavior of interface. Series of numerical experiments are performed to study the macroscopic stress–strain relationships and microscale damage evolution in MMCs under different loading conditions. An agreement between the simulation results and the experimental data is obtained.

Boundary element simulation of fatigue crack growth in multi-site damage

This paper presents an efficient and automatic scheme for modelling the growth of multiple cracks through a two-dimensional domain under fatigue loading based on linear elastic fracture mechanics. The dual boundary element method is applied to perform an analysis of the cracked domain and the J -integral technique is used to compute stress intensity factors. Incremental crack propagation directions are evaluated using the maximum principal stress criterion and a combined predictor–corrector algorithm implemented for propagation angle and increment length. Criteria are presented to control the mesh used on the slower growing cracks in the domain, improving computational efficiency and accuracy by the use of virtual crack tips to avoid the need for severe mesh grading. Results are presented for several geometries with multi-site damage, and sensitivity to incremental crack length is investigated. The scheme demonstrates considerable advantages over the finite element method for this application due to simplicity of meshing, and over other boundary element formulations for modelling domains with large ranges of crack growth rates.

Maximum tangential strain energy density criterion for general mixed mode I/II/III brittle fracture

The maximum tangential strain energy density criterion presented in the past for damage analysis of brittle materials under mixed mode I/II loading is extended to general mixed mode I/II/III in order to estimate the in-plane and out-of-plane fracture angles as well as the fracture load. The extended criterion is validated in all mixed modes I/II, I/III, II/III and I/II/III for both fracture angles and fracture loads using the experimental results reported in the literature. Good agreement is found between the results predicted by the extended maximum tangential strain energy density criterion and the experimental results. The theoretical results are also compared with those of the maximum principal stress criterion.

Numerical Simulation of Rock Fragmentation under the Impact Load of Water Jet

To investigate the rock fragmentation and its influence factors under the impact load of water jet, a numerical method which coupled finite element method (FEM) with smoothed particle hydrodynamics (SPH) was adopted to simulate the rock fragmentation process by water jet. Linear and shock equations of state were applied to describe the dynamic characteristics of rock and water, respectively, while the maximum principal stress criterion was used for the rock failure detection. The dynamic stresses at the selected element containing points in rock are computed as a function of time under the impact load of water jet. The influences of the factors of boundary condition, impact velocity, confining pressure, and structure plane on rock dynamic fragmentation are discussed.

The all-ceramic, inlay supported fixed partial denture. Part 5. Extended finite element analysis validation

This study is the last in a series detailing an investigation into the all-ceramic, inlay supported fixed partial denture, the major concern of which has been the examination of the stress responses of the bridge via the use of finite element analysis (FEA) and its validation. The progression from a classic FEA to the current extended or enriched FEA (XFEA) will be described and the validation performed. XFEA modelling was compared and validated against the experimental model analysis (EMA) as described in a previous study. The two EMA load case fracture strengths of 160 N and 313 N compared favourably with the best two fracture predictions from the XFEA of 185 N and 213 N (maximum principal stress criterion) respectively, with the origin of fracture and overall trajectory and pattern of crack propagation agreeing very well. XFEA load prediction is within 15% of the EMA in the best case. The sensitivity of the bridges to loading position variations was accurately predicted by the XFEA, together with the change in fracture origin from the molar to premolar embrasures. With this, the authors believe that they have provided a convincing validation, both qualitatively and quantitatively, of an anatomically realistic dental bridge.

Mixed mode crack growth simulation with/without overloads

In the present paper, mathematical models/procedures are developed in order to investigate the mixed mode crack growth process. The proposed procedures examine the fatigue life estimation and the crack path simulation under either constant amplitude loading or single overload. The fatigue life up to failure is calculated by employing two-parameter driving force model together with the equivalent stress intensity factor. The overload effect is theoretically analyzed by introducing the Wheeler’s retardation parameter. Further, the crack extension under Mode I/II conditions is experimentally investigated for two cracks emanating from two holes in the plate. Then, for the same mixed mode situation with two cracks, the crack growth paths are modeled by using the maximum principal stress criterion and the finite element method. The authors employ analytical and numerical approaches for the stress intensity factor calculations. The numerical investigation is performed by applying quarter-point (Q-P) singular finite elements. The efficiency of proposed procedures is verified through available crack growth data. The different mixed mode calculations are in a good correlation with crack growth observations.

Finite Element Simulation on Thermal Fatigue of a Turbine Blade with Thermal Barrier Coatings

In this paper, a finite element model was developed for a turbine blade with thermal barrier coatings to investigate its failure behavior under cyclic thermal loading. Based on temperature and stress fields obtained from finite element simulations, dangerous regions in ceramic coating were determined in terms of the maximum principal stress criterion. The results show that damage preferentially occurs in the chamfer and rabbet of a turbine blade with thermal barrier coatings and its thermal fatigue life decreases with the increase of thermal stress induced by high service temperature.