Damage Accumulation Process Research Articles

APPLICATION OF THE UMAT SUBROUTINE FOR SOLVING CONTINUUM MECHANICS PROBLEMS (OVERVIEW)

This paper presents an overview of the application of the UMAT subroutine of the SIMULIA Abaqus multifunctional software package in solid mechanics and related areas. This subroutine is used to describe new user materials that are not available in the class of standard materials of the SIMULIA Abaqus package. This overview article provides examples of problems and constitutive equations of materials that are modeled using UMAT / VUMAT procedures. Various types of materials are presented, successfully described by means of user-defined UMAT and VUMAT procedures. A general description and experience of using the UMAT subroutine is given. The results of finite element modeling of the deformation of aplate weakened by a central circular hole under uniform and uniaxial tension with steady-state creep in a damaged medium evolving according to a power law are presented in the coupled formulation of the problem (creep - damage). The distributions of stresses, strains, and damage fields at the tip of the defect under creep conditions are found, and an analysis is made of the effect of the damage accumulation process on the stress fields at the crack tip under steady-state creep conditions. The distributions of stresses and creep strains are demonstrated taking into account the accumulation of damage over time.

Damage analysis of a SiCf/SiC ceramic matrix composite under stepwise fatigue loading with acoustic emission

Continuous fiber-reinforced ceramic matrix composites (CMCs) exhibit different damage mechanisms at multiple scales under cyclic loading. In this paper, the tension-tension fatigue behavior of a plain woven SiCf/SiC CMC was investigated, and damage accumulation and evolution process were studied in detail via acoustic emission (AE) method. With the increase of cycles, the material exhibits obvious hysteresis behavior affected by interfacial slip and wear mechanisms. Most of the fibers with radial fracture characteristic have relatively high strength, showing excellent toughening property. In the stepwise cyclic loading process, the Kaiser effect of AE determines the initiation of AE activities at each initial loading moment, which shows obvious nonlinear damage accumulation behavior of the material. High-energy events are related to significant matrix cracking and fiber fracture, and the evolution process of material damage initiation and propagation is monitored in real time.

Study on compressive mechanical properties of recycled aggregate concrete with silica fume at different strain rates

Treating waste concrete to produce recycled aggregate concrete (RAC) is an important measure to save resources and protect environment. Studies have shown that adding silica fume to RAC can improve the mechanical properties of RAC. Based on the experiment, the uniaxial compressive mechanical properties of RAC specimens with silica fume content (S) for 0%, 5% and 9% at strain rates of 10−5/s, 10−4/s, 10−3/s and 10−2/s were studied. From the mesoscopic point of view, the damage and failure mechanisms of RAC were analyzed based on the statistical damage constitutive model. The results showed that with the increase of strain rate, the peak stress, elastic modulus and brittleness of RAC were on the rise. In addition, the peak stress and elastic modulus of RAC with high silica fume content were higher than those of RAC with low silica fume content. Considering two damage evolution modes of mesoscopic fracture and yield, the variation characteristics of mesoscopic damage parameters were obtained. From the perspective of effective stress, the whole process of damage evolution and accumulation induced catastrophe of concrete was expounded. The critical state and peak nominal stress state were distinguished, and it is considered that the critical state should be the limit state of the stress process of concrete material. These results were evaluated and analyzed by acoustic emission (AE), scanning electron microscope (SEM) and nuclear magnetic resonance (NMR) tests.

The effect of the fatigue damage accumulation process on the damping and stiffness properties of adhesively bonded composite structures

Wind turbine blade spar cap to shear web adhesively bonded connections can suffer from damage at the bond-line which can propagate through the structure compromising blade integrity. This study investigates changes in the stiffness and damping of a thick adhesive joint test specimen during a fatigue test. The stiffness is calculated using an extensometer and damping is determined using vibration and thermography. Fatigue tests showed three distinct phases of damage. Firstly, transverse cracks and delamination initiate and grow with little change in stiffness observed while damping increases by 18.6% and 17.8% inferred from the vibration and thermographic methods, respectively. In the second phase, the number of transverse cracks increases reaching saturation and the stiffness reduces by 4.7%. The increase in the loss factor is 65.7% and 95.6% from the vibration and thermographic methods, respectively. In the final phase, the crack density remains constant whilst de-bonding of the joint begins and grows until failure. The loss factor increases by 111.4% and 116.9% from the vibration and thermographic methods, respectively though the stiffness shows a cumulative reduction of only 8.6%. The results show the potential for monitoring changes in damping to infer incipient damage in an adhesively bonded composite joint structure.

Metallic materials fatigue behavior: Scale levels and ranges of transition between them

The metal fatigue behavior is analyzed on the basis of the multi-scale description of damage accumulation processes in direction of increasing scales (from micro- to meso- and macroscopic scale levels). The governing mechanisms in the damage accumulation process peculiar to each scale level are considered. The transitions between scales are realized gradually within the ranges with the bimodal distribution of fatigue life. Statistical analysis of data on mechanical characteristics defined in monotonic tensile and fatigue tests for aviation structural materials based on Fe, Al, Mg, Ti, Cu, and Ni have shown that for most alloys the three scale levels are exhibited in the direction of the stress level increasing.

ПОСТРОЕНИЕ ПОВЕРХНОСТИ ПАМЯТИ ДЛЯ РАЗДЕЛЕНИЯ ПРОЦЕССОВ МОНОТОННЫХ И ЦИКЛИЧЕСКИХ НАГРУЖЕНИЙ

Non-stationary and asymmetric processes of cyclic deformation are considered, which consist of a sequence of monotonic and cyclic loading modes, in which peculiar effects of landing and ratcheting of plastic hysteresis loops occur. Mathematical modeling of such processes of deformation and damage accumulation is based mainly on variants of plasticity theories belonging to the class of theories of plastic flow with combined (isotropic and anisotropic) hardening. In this paper, mathematical modeling of the processes of deformation and damage accumulation is based on a variant of the theory of plasticity – the Bondar model. Based on the analysis of the results of experimental studies of samples of stainless steel 12Х18Н10T under a rigid (controlled deformation) deformation process, which is a sequence of monotonic and cyclic loading modes, under conditions of uniaxial tension-compression at normal temperature, the features and differences in the processes of monotonic and cyclic loading are revealed. To describe these features and separate the processes of monotonic and cyclic loading modes in the theories of plastic flow with combined hardening, various variants of memory surfaces are introduced. An analysis of the results of experimental studies of stainless steel showed that in the space of the plastic strain tensor, the size of the memory surface is determined by the range of plastic strains, and the position of the center is determined by the values of average plastic strains under cyclic loading. Various variants of the memory surface are considered, their capabilities and disadvantages are identified, and proposed variant of the memory surface.To confirm the operability of proposed version of the memory surface, together with the equations of the Bondar plasticity model, the calculated and experimental results were compared and a reliable agreement was obtained between these results both in terms of the kinetics of the stress-strain state and in terms of the number of cycles to failure.

AE Characterization of damage in flexible solar cells under torsional loading

Torsional tests of flexible solar cells were conducted to evaluate the electrical performance degradation caused by mechanical loading. To elucidate the degradation mechanism of solar cells, it is indispensable to detect the damage initiation and accumulation due to the applied mechanical loading and to identify which of the damage contributes to the electrical performance degradation. Therefore, the AE technique was used to monitor the damage initiation and accumulation process, and the LT method, which can detect the temperature modulation caused by leakage current generation, was used to identify the damage that contributes to performance degradation. It was shown from AE measurement that damage which is a precursor of electrical performance degradation were detected. It was also found that the damage caused by tensile stress, which was dominant at the specimen ends, contributes the initiation of performance degradation. In addition, damage caused by the principal stress near the center of the specimen, which is inclined at 45° to the specimen length direction, was also suggested to cause significant performance degradation. Consequently, it was demonstrated that the electrical performance degradation processes of flexible solar cells under torsional loading.

МАЛОЦИКЛОВАЯ УСТАЛОСТЬ ОБРАЗЦОВ С КОЛЬЦЕВОЙ ВЫТОЧКОЙ ПРИ ЖЕСТКОМ НАГРУЖЕНИИ

The results of tests of cylindrical specimens of alloy 01570C for low-cycle fatigue are presented. The tests were carried out on a smooth sample and samples with an annular recess. Specimens with an annular groove were tested under rigid cyclic alternating loading with a constant range of elongation of the working part. To simulate the experiments performed, a variant of the plasticity model based on the theory of flow under combined hardening is used. In the chosen mathematical model, a memory surface is introduced that separates monotonous and cyclic loading. This division allows one to take into account various features of isotropic and anisotropic hardening of the material. Anisotropic hardening is described by the sum of backstresses of three different types, which make it possible to describe the effects of fitting and stepping out of the elastoplastic hysteresis loop. The plasticity model makes it possible to assess the damaged state of a material using an equation that describes the process of damage accumulation based on the energy criterion of durability. According to the results of testing a smooth sample, the parameters of the plasticity model were determined. The finite element method was used to carry out mathematical modeling of experiments on loading samples with an annular groove. The material behavior model was implemented in the SIMULIA Abaqus software package, for which the model equations were linearized and the Jacobi matrix was calculated, which determines the change in each of the stress increment components caused by an infinitesimal change in each component of the strain increment tensor. Based on the results of mathematical modeling, the dependences of the load applied to the sample on the elongation of its working part were obtained. The article compares the dependences of the load applied to the sample, obtained from the results of the calculation, with the experimental ones, as well as the number of cycles until the destruction of the sample.

A Statistic Damage Model of Rocks considering the Effect of Loading Rate

This paper develops a new statistic damage model for rock to mainly study the effect of a loading rate on its mechanical behaviours. The proposed model adopts a new loading rate‐dependent damage density function and is capable of describing the macroscopic damage accumulation process for rock samples subjected to external high‐speed dynamic loadings. The proposed model can also account for the residual strength of rocks by introducing a modified equivalent strain principle, which considers the contribution of the friction force to the strength of rocks. The friction force is generated by the movements of the nearby microcracks. The predicted stress‐strain curves by the proposed model agree with the measured data of salty rock under the conditions of various confining pressures and loading rates. It can be found that both the peak strength and the corresponding axial strain are increased at high‐speed loading conditions. At the same time, a transition from ductile failure to brittle failure can be observed in rock samples.

ОЦЕНКА РЕСУРСНЫХ ХАРАКТЕРИСТИК ПОЛИКРИСТАЛЛИЧЕСКИХ КОНСТРУКЦИОННЫХ СПЛАВОВ ПРИ ДЕГРАДАЦИИ ПО СОВМЕСТНЫМ МЕХАНИЗМАМ УСТАЛОСТИ И ПОЛЗУЧЕСТИ МАТЕРИАЛА

The problem of assessing the resource characteristics of responsible engineering facilities, taking into account the peculiarities of operational loading conditions, is discussed. The processes of degradation of the initial strength properties of structural materials (metals and their alloys) under combined fatigue and long-term strength mechanisms are considered. A mathematical model describing the processes of cyclic viscoplastic deformation and accumulation of fatigue damage in structural alloys under multiaxial disproportionate modes of combined thermomechanical loading has been developed from the modern positions of mechanics of the damaged medium and fracture mechanics. The model consists of three interrelated components: relations determining the cyclic viscoplastic behavior of the material, taking into account the dependence on the destruction process; evolutionary equations describing the kinetics of the damage accumulation process; criteria for the strength of the damaged material. The variant of the cyclic determining relations is based on the idea of the existence of plasticity and creep surfaces in the stress space and the principle of gradiency of the velocity vectors of plastic deformations and creep deformations to the corresponding surface at the loading point. These equations of state reflect the main effects of the process of cyclic viscoplastic deformation of the material for arbitrary complex loading trajectories. The variant of kinetic equations of damage accumulation is based on introduction of a scalar damage parameter and on energy principles. Ittakes into account the main effects of formation, growth and fusion of microdefects under arbitrary complex modes of combined thermomechanical loading. A joint form of the evolutionary equation of damage accumulation in the areas of low-cycle fatigue and long term strength is proposed. As a criterion of the strength of the damaged material, the condition of reaching the critical value of the damage value is used. The results of numerical modeling of deformation processes and damage accumulation in structural alloys with degradation mechanisms combining fatigue and long-term strength of the material are presented. The results of the comparison of calculated and experimental data showed that the proposed model of the mechanics of the damaged medium qualitatively and with the accuracy necessary for practical calculations quantitatively describes the processes of destruction of hazardous areas of structural elements under the combined actions of degradation mechanisms of fatigue and long-term strength.

Study of Radiation Embitterment and Degradation Processes of Li2ZrO3 Ceramic under Irradiation with Swift Heavy Ions

The work is devoted to the study of radiation damage and subsequent swelling processes of the surface layer of Li2ZrO3 ceramics under irradiation with heavy Xe22+ ions, depending on the accumulation of the radiation dose. The samples under study were obtained using a mechanochemical synthesis method. The samples were irradiated with heavy Xe22+ ions with an energy of 230 MeV at irradiation fluences of 1011–1016 ion/cm2. The choice of ion types is due to the possibility of simulating the radiation damage accumulation processes as a result of the implantation of Xe22+ ions and subsequent atomic displacements. It was found that, at irradiation doses above 5 × 1014 ion/cm2, point defects accumulate, which leads to a disordering of the surface layer and a subsequent decrease in the strength and hardness of ceramics. At the same time, the main process influencing the decrease in resistance to radiation damage is the crystal structure swelling as a result of the accumulation of defects and disordering of the crystal lattice.

Theories of plasticity under complex loading along spatial trajectories of deformations

Variants of theories of plastic flow with combined hardening, which are widely used in practical calculations of structures, are considered. A comparative analysis of variants of the theory under complex loading along the spatial trajectories of deformations of constant and variable curvature and torsion is carried out. The trajectories of large curvature and from medium to large torsion are considered. The analysis of the research results is carried out in the vector space of A.A. Il’yushin. The spatial trajectories of deformations in the form of helical lines of constant and variable curvature are considered. The calculation results are compared with the results of experimental studies on the response components of the stress vector and scalar properties along the deformation trajectory. Variants of the theory are considered: the Ishlinsky - Prager - Kadashevich - Novozhilov model (linear kinematic hardening and isotropic hardening); the Shabosh model with three evolutionary Armstrong - Frederick - Kadashevich equations; Themis model based on the invariant theory of plasticity; Bondar model with a three-term transformation of the evolutionary equation for kinematic hardening. Material parameters (functions) that close versions of the theory of plasticity are given. Satisfactory agreement with the experiment for all trajectories of deformations is achived when calculating on the basis of the Shabosh model - the difference between the results of calculations and experiments does not exceed 30 %. The best agreement with the experiment is achieved on the basis of the Bondar model - the difference between the results of calculations and experiments for all trajectories does not exceed 10 %. The Bondar Model is closed by three material parameters and one material function which are determined from simple experiments on uniaxial tension after preliminary compression (kink of the deformation trajectory by 180°). Bondar plasticity model has a generalization for non-isothermal loading, many features of cyclic disproportionate and proportional loading and describes the processes of damage accumulation (resource).

Influence of preliminary thermal aging on the residual interlayer strength and staging of damage accumulation in structural carbon plastic

Aging of composites is a pervasive problem that leads to mechanical properties degradation, reduced design life of a structure and premature accidental failure. The work is devoted to an experimental study of the preliminary temperature aging effect on the residual mechanical properties of structural CFRP. The joint use of test systems and systems for registration and analysis of acoustic emission signals was applied. The Short Beam Shear Test of CFRP specimens were carried out using the short beam method. The tests were carried out on universal electromechanical systems Instron 5882 and Instron 5965 in accordance with the recommendations of ASTM D2344. In the process of loading the samples were continuously recorded by using the acoustic emission signals system AMSY-6. A piezoelectric sensor with a frequency range of 300-800 kHz was used. The test and diagnostic systems were synchronized during the tests. In the course of the work the values of the interlayer shear strength were determined for the samples of CFRP. Typical types of the sample destruction are illustrated. When analyzing the change in the mechanical properties of the carbon fiber reinforced plastic from a temperature increase the critical values of temperatures were established in which a sharp decline in the strength and elastic characteristics of materials occurs due to an active destruction of the binder. The graphs of the energy parameter dependence and frequency characteristics of acoustic emission signals on time have been constructed and analyzed. The estimate of the processes of damage accumulation in composites is carried out. The change of the damage accumulation mechanisms was illustrated. The obtained results illustrate the effect of elevated temperatures and the duration of their impact on the mechanical behavior of structural CFRP specimens during the static tests for the interlayer shear.

Experimental study of the destruction in CFRP laminates at the macro-level by acoustic emission method

The author conducted experiments using the method of acoustic emission under uniaxial tension of specimens of CFRP laminates with different stacking, geometry and stress concentration. The influence of a mutual arrangement of the material destruction zone and the extensometer installation site on the nonlinear deformation is revealed. It is shown that the damage accumulation process is highly informative when determining the energy of AE pulses. The possibility of visualizing the formation and development of destruction zones in orthogonal directions, as well as the possibility of determining the moment of crack start from the apex of the notch during splitting, is established. The mechanism of alternating stress relaxation in two developed zones of destruction is revealed. The paper shows a high degree of correlation between mechanic and acoustic-emission events. Finally, the author suggests assessing the mechanical state of material with the account of obtained damages by the degree of its integrity (one to zero) depending on the load history, its individual geometric features and stress concentration.

Modeling of Fatigue Wear of Viscoelastic Coatings.

A new model for studying the kinetics of fatigue wear of a viscoelastic coating bonded to a rigid substrate is proposed. The fatigue mechanism is due to the cyclic interaction of the coating with a rough counterbody, which is modeled by a periodic system of smooth indenters. The study includes the solution of the problem of sliding contact of the indenter at a constant velocity along the viscoelastic coating, the calculation of stresses taking into account the mutual effect, and study of the process of damage accumulation in the material. The calculation of the damage function of the surface layer was carried out using the reduced stress criterion. Assuming the possibility of summation of accumulated damage, two processes were considered: delamination of surface layers of the coating and continuous fracture of the surface by the fatigue mechanism. The effect of the sliding velocity and viscoelastic properties of the material on the damage accumulation and the coating wear rate was analyzed. Two types of load, constant and stochastically varying, were used in modeling and analysis. It was found that the rate of fatigue wear of the coating increased and then became constant.

Damage and fracture prediction of 7075 high-strength aluminum alloy during cryogenic stamping process

In order to accurately predict the damage and fracture behaviors of a 7075 aluminum alloy during cryogenic stamping, a nonlinear damage model taking into account stress triaxiality and cryogenic temperature was established to access the formability of the alloy. Seven types of specimens with various stress triaxialities were tested and simulated to define a triaxial-failure curve, and the damage parameters of the model for 7075 alloy deformation at room temperature and liquid nitrogen temperature were determined by the inverse calibration method. Moreover, finite element simulations combined with this model were used to analyse the damage and fracture behavior of a U-shaped part stamped at low temperature. The results indicated that the alloy at −196 °C showed a remarkable improvement in failure strain. The damage value of the cryogenic deformed specimens was smaller than that at room temperature. It was found that the model was capable of predicting the nonlinear damage accumulation and cracking process of the cryogenic stamped part. A good agreement of the fracture onset and position were found between experiments and simulations. The cryogenic samples presented a combination of ductile-fracture modes and transgranular brittle fracture modes, which was significantly different from those at RT.

Novel Experimentation for the Validation of Mechanistic Models to Describe Cold Dwell Sensitivity in Titanium Alloys

Previous mechanistic models, proposed to explain the process of damage accumulation and stress redistribution between strong and weak regions inherent within the microstructure of α/β and near α titanium alloys, are validated through a matrix of experiments employing a non-standard variant of the alloy Ti 685. The grain size of the model material was deliberately processed to offer grains up to 20 mm in diameter, to facilitate constitutive measurements within individual grains. A range of experiments were performed under static and cyclic loading, with the fatigue cycle conducted under either strain or load control. Data will be reported to demonstrate significant variations in elastic and plastic properties between grains and emphasise the role of time dependent strain accumulation. Implications for the “dwell sensitive fatigue” or “cold creep” response of conventional titanium alloys will be discussed.

Characterization of piercing damage in CFRP cross-ply laminates after punch shear machining via impact loading

In industrial processes, piercing and trimming are essential because composite structures are usually manufactured in a near-net shape to reduce machining operations. Punching and shear cutting using out-of-plane shear loading are expected to increase productivity. Nevertheless, little is known about the effects of such operations on polymer-matrix composites. This study presents on the characterization of piercing damage in typical carbon fiber reinforced plastic (CFRP) cross-ply laminates [0°2/90°2]s after punching using quasi-static (QS) and drop-weight impact (DWI) loadings. During QS punching, the upper and lower ply interfaces delaminate due to the high shear stress to cut fibers and gradual shear deformation in the middle ply; however, during DWI punching at a low impact velocity, delamination of the lower ply interface can be reduced due to the localization of shear deformation, as compared to that in QS punching. Finally, the damage accumulation process during DWI punching is discussed.

Experimental Study of Fatigue Damage Accumulation in Laminated Carbon Reinforced Fiber Plastics

It is necessary to achieve high fatigue strength in order to apply carbon reinforced fiber plastics (CRFP) for critical elements subjected to vibration. Gradual accumulation of fatigue damage is accompanied by changes in the material stiffness and natural frequencies. The purpose of this work is to found experimental data on the change of the elastic characteristics of layered CRFP as fatigue damage accumulates. The object of the study is standard samples made of unidirectional carbon/epoxy fiber with different layering schemes. The samples were subjected to fatigue tests under cyclic tension with constant amplitude. The test of each sample was stopped several times at different loading stages to execute experimental modal analysis and non-destructive inspection of the appeared defects. The found natural frequencies were used to solve the inverse problem of identifying the elastic parameters of the laminate monolayer: two Young’s modulus, shear modulus and Poisson’s ratio. As a result, the dependences of these parameters on the relative fatigue life were obtained. These dependences, together with the results of non-destructive testing, can be used to describe the process of fatigue damage accumulation and for the subsequent development of methods for the fatigue life prediction.

Структурная модель деформирования и разрушения гетерогенных материалов типа сферопластика при действии гидростатического давления

Object and purpose of research. The paper investigates polymeric composite material of syntactic foams type being by nature a heterogeneous medium and consisting of polymeric matrix, filled with spherical inclusions: microspheres. The main purpose of this this paper is to develop a structural model of straining and failure for this type of materials under hydrostatic pressure and software and mathematical apparatus for model implementation. Materials and methods. The input data for this research were composition and structure of syntactic foam material as well as the performance of its components (polymeric matrix and glass microspheres). Structural model was developed on the basis of solutions to linear elasticity theory problems using Lubachevsky – Stillinger algorithm for the formation of structure, homonization methods, etc. A calculation algorithm implemented in code in the С++ language was developed on the basis of the designed mathematical apparatus. Verification of calculation results was carried out by comparison with failure test results of samples of one of the grades of syntactic foam under short-term hydrostatic pressure loading. Main results. Structural model of syntactic foam type material straining and failure under hydrostatic pressure was developed. A calculation algorithm implemented in program code written in the С++ language which is relatively highly efficient for analysis of real structures with a large number of microspheres of the order of 105. Correlation with experimental results showed compatibility of modelling results in terms of both quantitative and qualitative estimates. Conclusion. The developed structural model allows with a high degree of confidence to describe the processes of damage and failure accumulation in syntactic foam under hydrostatic pressure. For practical purposes the model can be used applied for prediction of syntactic foam performance (strength, bulk strain and buoyancy), based on the properties of the initial components – microspheres and polymeric matrix.