Damage Mechanics Model Research Articles

A model for ultra low cycle fatigue damage prediction of structural steel

Ultra low cycle fatigue (ULCF) damage of structural steel is an important failure mode in earthquakes. A modified continuum damage mechanics (CDM) model was proposed to predict the fatigue life for ULCF damage. To this end, the functional form of the reduction coefficient considering the effect of plastic strain was constructed. The constant of function form was fitted by ULCF tests and genetic algorithm. Finally, the accuracy of the modified CDM model was verified by ULCF tests. Results showed that the modified CDM model could reduce the relative error between the predicted and tested fatigue life.

Warp-loaded mechanical performance of 3D orthogonal layer-to-layer woven composite perforated structures with different apertures

Owing to the superior mechanical performance, 3D orthogonal layer-to-layer woven composites (3DOLWC) are being increasingly favored in structural design. Its perforated structure (called 3DOLWC-PS) is a typical component in engineering, but its mechanical behavior is not clear, especially with different apertures, which enormously limits the application of 3DOLWC. In this paper, we discuss the mechanism of meso-randomness through the characterization of 3DOLWC, and establish its random unit cell model. On this basis, a macro-meso finite element simulation model of 3DOLWC-PS is built. Subsequently, combined with a developed continuous damage mechanics model, 3DOLWC-PS is simulated and verified by experiments. The results demonstrate that the established macro-meso simulation model can precisely predict the mechanical properties of 3DOLWC-PS and effectively explore its failure behavior. Furthermore, with the aperture increases, the strength of 3DOLWC-PS decreases linearly, but its stiffness is almost unchanged. It is worth mentioning that the notched stress concentration effect only affect the initial damage, but has little effect on the subsequent damage propagation process. This work provides the theoretical guidance and points out the design direction for the application of 3DOLWC-PS, and has crucial engineering significance.

Insight into the role of interfaces on mechanical properties of low-porosity Al/Ni compacts: Comparison of experiment and simulation

Quasi-static uniaxial tension and compression, three-point bending, and Hopkinson bar measurements have been carried out on low-porosity Al/Ni compacts (pressed powders) as well as compacts of the constituent Al and Ni. Concurrently, mesoscale material point method (MPM) simulations of fully resolved Al, Ni, and Al/Ni compact microstructures and engineering scale MPM simulations of homogenized Al/Ni compacts have been conducted. These simulations, in conjunction with the experimental measurements, have allowed us to parameterize mesoscale particle/particle contact models and engineering scale anisotropic damage mechanics models for the materials. The goal of this coordinated experimental and simulation study of Al/Ni and its constituent materials was to better understand their mechanical properties and gain insight into the nature of Al–Ni and Al–Al interfaces in Al/Ni compacts and their impact on mechanical properties of the compacts. We found that brittle tensile failure of Al/Ni compacts was dominated by the strength of the Al–Al interface while ductile compressive behavior of Al/Ni compacts was largely determined by the behavior of the Al phase. The properties of both Al–Al interface and Al phase appear to be altered by the presence of Ni. Finally, it was found that softening resulting from shear damage offset underlying strain hardening of the Al and Ni phases during compressive loading of the Al/Ni compacts.

Damage mechanism and constitutive model of surface paste disposal of a coal mine collapsed pit in a complicated environment

The surface paste disposal (SPD) method can effectively stabilize active coal mine collapsed pits. The degradation mechanism of the mechanical properties of SPD materials in complicated environments has not yet been explored. To investigate the deterioration mechanism of SPD in complicated environments, SPD specimens prepared from coal gangue and a small amount of cement and water as raw materials were tested by freezing-thawing (FT) cycle tests, wetting-drying (WD) cycle tests and freeze-thaw corrosion (FC) tests. The damage evolution law was obtained by the macro- and microscale methods. Studies have shown that the unconfined compressive strength (UCS) of SPD decreases exponentially under FT and FC cycles and decreases linearly after 5 WD cycles. FT, FC and WD all resulted in cracks and holes in SPD. Ettringite (Aft) produced by sulphate corrosion, calcium chloroaluminate hydrate (Friedel's salt) produced by chloride corrosion, magnesium silicate hydrate (M-S-H) produced by magnesium salt corrosion, and thaumasite produced by low temperatures and bicarbonate corrosion are important reasons for SPD strength deterioration. A segmented statistical damage constitutive model with the compaction point as the critical point is established. The damage constitutive model can completely describe the SPD stress-strain curve after corrosion in a complicated environment. The research results can provide guidance for the paste disposal of coal mine collapsed pits.

Experimental and numerical investigations on the rotation capacity of high strength steel beams

AbstractIn order to design efficient and highly utilised sections, the plastic/plastic design approach depicts a valuable tool. Concerning plastic design, Eurocode 3 requires only Class 1 cross‐sections and material grades up to S460, depicting conventional strength steels (CSS), to be used. High strength steels (HSS) with yield strengths up to 700 MPa are not considered appropriate for plastic design due to their lower ductility. However, the exclusion of HSS appears to be unnecessary in the light of recent test results. Experimental investigations on 20 homogeneous and hybrid high strength double symmetric I‐section beams have been conducted comprising various slenderness characteristics of flange and web and different span lengths. The results show that the rotation capacity value of R = 3, currently required by EC3 regulations, can actually be achieved by high strength steel beams depending on their cross‐sectional characteristics. Additionally, the experimental tests have been recalculated numerically. The material characteristics of the models have been defined by flow curves, which have firstly been calibrated on the basis of small‐scale tensile tests and furthermore slightly fitted to the full‐scale test results. Ductile material failure in terms of crack initiation and evolution is considered by incorporating a damage mechanics model. It can be shown that experimental and numerical results show very good accordance.

Cumulative Shear Damage Mechanism to Short Fiber Type C/SiC

A cumulative damage mechanism for short fiber type C/SiC during shear loading–unloading testing was examined and quantified using Iosipescu specimens parallel in the in-plane and through-thickness plane, and by using modified fracture and damage mechanics theory referring to measured damage characteristics (crack length, number and angle). A nonlinear stress–strain relation was found for both specimens. Decrease in the apparent modulus was confirmed with increased peak stress, although permanent strain increased. Inelastic strain of the decomposed tensile direction derived from shear stress was greater than that of the compressive one. Cracks propagated perpendicularly to the tensile direction, intruding on the boundary of the transverse fibers and connecting to other cracks. The theoretical damage mechanics model succeeded to predict the stress–strain relation, proposing that the shear mechanical properties are predictable by measuring the damage characteristics.

Damage-mechanics mesoscale modeling of composite laminates considering diffuse and discrete ply damages: Effects of ply thickness

Thin-ply composites are gaining significant attention owing to their high damage resistance and their ability to enhance design flexibility in a composite structure. Herein we proposed a damage mechanics model considering diffuse and discrete ply damages in thin-ply composite laminates for mesoscale simulation. To investigate the effects of ply thickness on damage evolution, loading and unloading tests were conducted using cross-ply, angle-ply, and quasi-isotropic laminates with several ply thicknesses. The damage evolution was quantitatively evaluated using continuum damage mechanics. The evolution laws of damage were formulated considering the ply thickness dependency. A damage simulation using the proposed model demonstrated that the retardation and suppression effects of thin-ply were captured by the proposed model. The simulation results also validated that the stiffness degradation and failure strength of laminates with three different ply thicknesses were predicted with good accuracy by considering both diffuse and discrete damages.

A Three-Dimensional Finite Element Damage Mechanics Model to Simulate Fretting Wear of Hertzian Line and Circular Contacts in Partial Slip Regime

Abstract In this investigation, a three-dimensional (3D) finite element model (FEM) was developed to study fretting wear of Hertzian circular and line contacts. The wear law incorporated in this model is based on the accumulated dissipated energy (ADE). A stress-based damage mechanics finite element model using the ADE was developed to determine wear of non-conformal bodies in contact. Voronoi tessellation was used to simulate the microstructure of the materials during the fretting process. In order to simulate the wear area in fretting contacts, a material removal approach was developed and implemented in the model. The FEM was used to investigate partial slip regimes under various operating conditions. The normal and shear surface tractions for the circular and line contacts were applied to the domain in order to improve the computational efficiency. The calculated wear volume rate using the FE model is in good agreement with the wear coefficient available in the open literature. The influence of modulus of elasticity, hardness, and coefficient of friction on the partial slip fretting phenomenon were studied. In order to verify the model, several fretting wear tests were conducted using AISI 8620 steel and AISI 1566 steel in a partial slip regime of circular contact configuration. The properties for each material such as the modulus of elasticity, hardness, and the grain size were measured experimentally and compared with the model. For the defined load and displacement amplitude of the experimental fretting tests, both materials have shown a partial slip behavior in the initial cycles and then transition to a gross slip regime. The numerical model predicted the worn surface and wear-rate in partial slip regime which corroborated well with these experimental test results.

Experimental evaluation of the local failure criterion and its implementation in a damage mechanics model

Herein, a tensile test for notched round–bar specimens of two types of carbon steel used in nuclear containment vessels was performed. The test results were analyzed using the Bridgman solution and an elastoplastic finite element method. The analyses showed that ductile failures in the tensile state were initiated when the sum of equivalent and mean stresses reached a critical value of the material. A simple analysis of local failure for a nuclear containment was conducted using the failure criterion, and its engineering effectiveness was then discussed. The criterion is consistent with Argon's void nucleation model and can be implemented into the void nucleation term of stress control in the Gurson–Tvergaard (GT) model. The simulation performed using the GT model, which applied the limit value of the sum of equivalent and mean stress obtained from the tensile tests to the void nucleation term, successfully reproduced failure behaviors in the specimens.

Mechanical behaviors and damage model of expansive soil admixed with composite materials

Mechanical behaviors and damage model of expansive soil admixed with composite materials

A modified phase field model for predicting the fracture behavior of quasi‐brittle materials

AbstractPhase field models have a very good capability in predicting the crack path, but most of them represent the dependence of the regularization parameter on the load‐carrying capacity of structures. In this paper, a phase field model is coupled with isotropic damage model aiming to resolve this issue in the fracture simulations of quasi‐brittle materials. Damage variables are calculated by a continuum damage mechanics model based on accurate energy reduction and then regularized by the phase field model. Since the continuum damage mechanics model is combined with phase field method, tensile strength of material is employed for calculating the damage field and phase field. Our approach can predict the accurate load‐carrying capacity independent of the regularization parameter while maintaining the precision of the crack path prediction. Three benchmark problems are solved to demonstrate good performance of our approach, and results are compared with those by the damage mechanics model or by the standard phase field model.

Effects of characteristic element length on fracture energy dissipation in continuum damage mechanics models

Progressive damage finite element (FE) analysis methods based on continuum damage mechanics (CDM) use mesh regularization algorithms to ensure that fracture energy dissipation predictions are independent of problem discretization. Mesh regularization algorithms require some geometric input related to the discretization. When using crack band theory for mesh regularization, a characteristic element length is used to approximate the width of the region affected by the continuum crack, i.e., the crack band width. Inaccuracy in representing the crack band width significantly affects predictions in terms of fracture energy dissipation. For square elements misaligned by 45°, using a typical line length across an element rather than the crack band width overestimates dissipated fracture energy by 41%. Not accounting for element aspect ratio underestimates dissipated fracture energy by 29% and 50% for ratios of two and four, respectively. Herein, methods for calculating characteristic element lengths in fiber-reinforced materials are presented that account for meshes being misaligned with respect to material directions, element aspect ratio, and element skew. The limits of applicability of different crack band width approximations are explored through numerical crack growth studies and center notch tension FE analyses for different discretizations. Results are compared in terms of fracture energy dissipation to linear elastic fracture mechanics. Analyses with the proposed characteristic element lengths predict consistent fracture energy dissipation with various meshes. The proposed methods and the included studies on potential error in fracture energy dissipation provide analysts the basis to better understand error in CDM model predictions associated with simplified FE model preprocessing.

A Continuum Damage Mechanics-based Piecewise Fatigue Damage Model for Fatigue Life Prediction of Fiber-Reinforced Laminated Composites

The purpose of this study is to define a piecewise fatigue damage model (PFDM) for the prediction of damage in composite laminates under cyclic loading based on the continuum damage mechanics (CDM) model. Assuming that damage in fiber-reinforced plastic structures accumulates nonlinearly, a piecewise degradation growth function is defined and coupled with CDM and micromechanics approaches. The model divides the damage behavior of fiber, matrix, and fiber/matrix debonding at the ply scale, into three different stages. For generality, a fully multi-stage damage formulation on a single-ply level is employed. The unknown parameters of the PFDM are estimated according to obtained experimental data of damage mechanisms associated with the composites laminate under cyclic loading. To predict multidirectional composite laminates' fatigue life, the proposed model was implemented in Abaqus software by the subroutine. In a validation against experimental data on carbon fiber reinforced material, the model proves to provide a good numerical approximation of the damage during the fatigue loading. The results reveal that by considering the multi-stage process in stiffness reduction, the proposed model can estimate the fatigue life of composite laminate under multiaxial cyclic loading conditions more accurately than the similar model in the literature.

Bearing strength and failure behaviour of composite pre-tightened multi-tooth joint

The bearing strength and failure behaviour of a new composite pre-tightened multi-tooth joint was studied experimentally and numerically. Four groups of different types of specimens were fabricated by varying key design variables including the pre-tightening force, tooth depth, tooth length, and number of teeth. Axial tensile tests were performed to determine the bearing capacity, failure modes, and load distribution law of the specimens. Furthermore, a three-dimensional continuum damage mechanics (CDM) model was established based on the Pinho theory and nonlinear shear constitutive model. Finally, the corresponding numerical results were compared with the experimental results and demonstrated good agreement. The results indicated that in a certain range, the bearing capacity of the joints increased with an increase in the pre-tightening force, tooth depth, tooth length, and number of teeth. The designed multi-tooth joint has four typical failure modes: crushing failure, shear failure, longitudinal splitting failure, and fibre breakage. The load distribution ratio of each tooth of the joint is non-uniform, and it is significantly affected by the number of teeth and failure mode. The comparisons among the experimental and numerical results indicated that the CDM model is effective for predicting the bearing strength and failure behaviour of the multi-tooth joints.

Characterization of ductile fracture criterion for API X80 pipeline steel based on a phenomenological approach

Steel pipelines for oil/gas transportation might be subjected to large plastic strain under extreme loading conditions, which will lead to localized fracture. The damage mechanics model is a promising tool to perform most of the assessment analysis and evaluation at the simulation level. In this paper, a micro-based Gurson-Tvergarrd-Needleman (GTN) model and two recently proposed uncoupled fracture criteria, modified Mohr-Coulomb (MMC) criterion and extended Rice-Tracey (ERT) criterion are evaluated using API X80 steel. A comprehensive experimental study including five different notched specimens covering a wide range of stress triaxiality and lode dependence is conducted. Corresponding finite element models are established. A phenomenon-based hybrid numerical-experimental calibration method is used to determine the fracture parameter for these three models. Then the calibrated parameters are validated through notched tensile tests and compact tension (CT) tests. It is shown that the presented fracture criteria are in a good capability to characterize the ductile fracture behaviors of API X80 pipeline steel.

Hierarchical microstructure based crystal plasticity-continuum damage mechanics approach: Model development and validation of rolling contact fatigue behavior

A microstructure-based integrated crystal plasticity (CP) and continuum damage mechanics (CDM) model is proposed for simulating rolling contact fatigue (RCF). The damage process through the formation of the dark etching region (DER) under RCF is implemented, i.e., a DER-CPCDM approach. A hierarchical microstructure of lath martensite is virtually generated by the Voronoi tessellation technique and the theoretical Kurdjumov-Sachs orientation relationship between the prior austenite grains and substructures of lath martensite. Moreover, the micro-plasticity calculated from the polycrystal finite element is coupled with dislocation-assisted carbon migration theory, which enables accurate predictions of the deformation inhomogeneity and the DER/damage distribution at the subsurface. The RCF lifespan of AISI 52100 bearing steel can be predicted within reasonable accuracy, in terms of Weibull probability analysis, when the jump-in-cycles approach is implemented in the DER-CPCDM model. The predicted representative lifespan of the Weibull plot is within an error of 13% when compared with reported experimental data. Process factors, including contact pressure, rotational speed, temperature, carbon concentration, and grain size, are analyzed in a numerical sensitivity study, which can be utilized for potential optimization of the RCF process for improving the performance of materials and parts.

Effect of ellipse motion paths with different aspect ratios on friction and wear of highly crosslinked polyethylene

Cobalt chromium molybdenum alloy and highly cross-linked polyethylene are selected as the counterpairs in this study to carry out friction and wear testing over different ellipse motion paths to explore the influence of ellipse motion path on friction and wear of prosthesis materials. Here, the analytical methods for the periodic friction coefficient and special point wear are proposed to investigate the relationship between motion paths and tribological properties. The damage mechanism model of high cross-linked polyethyleneunder ellipse motion paths was established, which revealed the connection among material composition, motion paths and friction and wear mechanism. The results show that the friction coefficient and wear morphology are directly affected by changes in motion paths. The friction coefficient decreases with increasing aspect ratios, and the wear profile depth increases with increasing aspect ratios. The spatially resolved friction coefficient curve distinctly exhibits periodic “W”-type variation in elliptical motion paths. The friction coefficient shows maximum values at the long-axis endpoints and minimum values at the short-axis endpoints. There are different wear morphologies in different characteristic areas over the elliptical wear paths. The wear profile depth and width at the long-axis endpoints are larger than those at the short-axis endpoints, and the wear morphology is also more serious.

Modelling the asymmetric tension–compression properties of additively manufactured alloys using continuum damage mechanics

Additively manufactured parts often comprise internal porosities due to the manufacturing process, which needs to be considered in modelling their mechanical behaviour. It was experimentally shown that additively manufactured parts’ tensile and compressive mechanical properties are different for various metallic alloys. In this study, isotropic continuum damage mechanics is used to model additively manufactured alloys’ tension and compression behaviours. Compressive stress components can shrink discontinuities present in additively manufactured alloys. Therefore, the crack closure effect was employed to describe different behaviours during uniaxial tension and compression tests. A finite element model embedded in an ABAQUS’s UMAT format was developed to account for the isotropic continuum damage mechanics model. The numerical results of tension and compression tests were compared with experimental observations for additively manufactured maraging steel, AlSi10Mg and Ti-6Al-4V. Stress–strain curves in tension and compression of these alloys were obtained using the continuum damage mechanics model and compared well with the experimental results.

Effect of tunneling cracks on structural property degradation of wind turbine blades

In this study, a multi-scale structural approach is used to analyze the effect of tunneling cracks on the structural response of wind turbine blades. In this approach, a 2D finite-element-based cross-section analysis and a continuum damage mechanics model are combined to efficiently predict the variation in cross-section stiffnesses and natural frequencies of the blades as a function of the tunneling crack density. By applying this approach to an 86.35-meter wind turbine blade, it is shown how the level of variation of these structural properties depends not only on the degradation of the material properties due to the presence of tunneling cracks but also on the spatial characteristics of the different cross-section regions along the blade, such as spar caps, trailing-edge panels, etc.

Experimental and numerical investigations of tensile specimens containing multiple flaws in the ductile-to-brittle transition region

In thick-walled ferritic steel forgings, a large number of flaws can arise due to an unfavorable chemical composition or an erroneous heat treatment. Thus, a comprehensive understanding of the interaction of multiple flaws and their failure mechanisms is necessary.In this paper, experimental and numerical results from tensile specimens containing multiple flaws nearly parallel to the loading direction are presented. The material used for these investigations is the ferritic pressure vessel steel 22NiMoCr3-7, which is similar to an SA 508 Cl.2 steel. The experiments were conducted in the upper and in the lower shelf of the ductile-to-brittle transition region of fracture toughness. In addition, several specimens were tested to determine the material characteristics and to examine the fracture mechanisms for different levels of stress triaxiality.For numerical evaluations, damage mechanics models were used to investigate flaw interaction and the fracture mechanisms. In the upper shelf, an extended non-local Rousselier model was used. The numerical investigations in the lower ductile-to-brittle transition region were carried out with a coupled damage mechanics model. This coupled model consists of the extended non-local Rousselier model and an extended Beremin model, which was newly developed. The modifications of the models are accounting for low stress triaxiality and mixed fracture (dimple and cleavage fracture).A comparison between the numerical und experimental results shows that the defined damage mechanics models are able to describe the deformation and failure behavior of the tested specimens with a high accuracy. The investigations show that the flaw interaction behavior is strongly dependent on the temperature and the arrangement of the cracks. In the upper shelf, the crack growth is shear-stress dominated, whereas in the lower ductile-to-brittle transition region the crack growth is preferably normal to the loading direction.