Function Of Stress Triaxiality Research Articles

감육배관 손상시험 결과를 이용한 국부손상기준 검증

The objective of this study is to validate local failure criteria, which were proposed based on the notched-bar specimen tests combining with finite element (FE) simulations, using the results of real-scale pipe failure tests. This study conducted burst test using wall-thinned pipe specimens, which were made of 4 inch Sch.80 ASTM A106 Gr.B carbon steel pipe, under simple internal pressure at ambient temperature and performed associated FE simulations. Failure pressures were estimated by applying the failure criteria to the results of FE simulations and were compared with experimental failure pressures. It showed that the local stress based criterion, given as true ultimate tensile stress of material, accurately estimated the failure pressure of wall-thinned pipe specimens. However, the local strain based criterion, which is fracture strain of material as a function of stress tri-axiality, could not predict the failure pressure. It was confirmed that the local stress based criterion is reliably applicable to estimation of failure pressure of local wall-thinned piping components.

Explicit Finite-Element Analysis of 2024-T3/T351 Aluminum Material under Impact Loading for Airplane Engine Containment and Fragment Shielding

Uncontained aircraft engine failure can cause catastrophic damaging effects to aircraft systems if not addressed in the aircraft design. Mitigating the damaging effects of uncontained engine failure and improving the numerical modeling capability of these uncontained engine events are crucial. In this paper, high strain rate material behavior of one of the most extensively used materials in the aircraft industry is simulated and the results are compared against ballistic impact tests. Ballistic limits are evaluated by utilizing explicit finite-element (FE) simulations based on the corresponding ballistic impact experiments performed at different material thicknesses. LS-DYNA is used as a nonlinear explicit dynamics FE code for the simulations. A Johnson–Cook material model with different sets of parameters is employed as a thermo-viscoplastic material model coupled with a nonlinear equation of state and an accumulated damage evaluation algorithm for the numerical simulations. Predictive performance of the numerical models is discussed in terms of material characterization efforts, material model parameters, mesh sensitivities, and effects of stress triaxiality. It is shown that mesh refinement does not necessarily provide better results for ballistic limit simulations without considering and calibrating these interrelated factors. Moreover, it is shown that current models that can only fit a specific function for damage evaluation as a function of stress triaxiality are not always successful in predicting failure, especially if the state of stress changes significantly.

Deformation Analysis of Shearing Process Using Results of Notched Round Bar Tension Test

Deformation analysis of shearing process is carried out by using finite element method (FEM). Gurson-Tvergaard-Needlman (GTN) model is applied as a fracture criterion because ductile fracture behavior is a dominant factor in shearing process. Ductile fracture involves micro void nucleation, growth and coalescence of voids. To predict void nucleation in FEM analysis, a void nucleation critical strain model is proposed. Furthermore a notched round bar tension test using image analysis is proposed for deciding material properties relating ductile fracture. Gradual changes in the necking shape and tensile load are measured by using the test. From the results, strain and stress history at the necking section of tensile specimen and relationship between stress triaxiality and microvoid nucleation are obtained. Additionally, obtained damage parameters are introduced to the deformation analysis of shearing process and the results are compared with the experimental result. (doi:10.2320/matertrans.MF200903) Shearing process is used to cut off material by using punch, die and blank holder. This process is widely applied to make the billet in forging and electronic terminal parts and so on. Sheared surface has smooth area (sheared surface) which is made by metal flow in punch-die clearance, rough area (fracture surface) which is appeared by crack initiation and propagation at the tip of punch and die, burr and shear drop. These shape factors affect precision and quality of products, thus some researchers investigated the influence of process conditions on the shape of sheared surface. 1,2) Over the past few years, several studies have been performed on deforma- tion analysis of shearing process using finite element method (FEM), because the technology of CAE (Computer Aided Engineering) and computer performance has been pro- gressed. 3-5) On the shearing process, separation of material is completed by ductile crack connection which is generated at the tip of punch and die. Because sheared part shape is affected by the ductile fracture behavior, crack generation and propagation, optimum fracture criterion has to be used in FE analysis of shearing process. Ductile fracture involves micro void nucleation, growth and coalescence of voids. Micro voids appears on the inclusion-matrix boundary, grain boundary and in grain. Next, they grow with large plastic deformation of matrix material, and coalesce into macroscopic crack. In shearing process, sheared surface shape is affected this ductile crack behavior, and it has to be simulated in FE analysis using optimum ductile fracture criterion. In this study, Gurson- Tvergaard-Needlman model (GTN model) is applied to analysis of shearing process as a fracture criterion because this model express above micro voids behavior. There are some researches in which GTN model is applied to FE analysis of shearing process and the results show that GTN model is available for shearing analysis. 6-8) There are several material properties in GTN model and void nucleation critical strain is one of them. This parameter means that void nucleation is occurring when material strain reaches void nucleation critical strain. In the past studies, void nucleation critical strain is treated as a constant material value. However, it is known that stress state affects the nucleation and growth of micro voids. 9) In this study, new void nucleation critical strain model is proposed. In this model, void nucleation critical strain is expressed by a function of stress triaxiality and it is necessary to obtain the relationship between the stress triaxiality and void nucleation strain from some kind of material tests. For the purpose, notched round bar tension test using image analysis was developed and carried out. In this test, the specimen which has a circumferential notch was tensile and its notch curvature radius change was captured by CCD camera from the start of the test until material fracture continuously. It is possible to obtain a history of stress triaxiality and equivalent strain in notch center of specimen using the image analysis result of the notch shape change. From the results, material properties relating ductile fracture in the void nucleation critical strain model and GTN model were determined and introduced FE code we designed. Deformation analysis of shearing process is performed, and its accuracy is evaluated comparing experimental result. In this consideration, reli- ability and availability of proposed models are also inves- tigated.

Investigation of Local Failure Criteria of Wall-Thinned Area by Simulated Specimen Tests

The objective of this study is to develop a local failure criterion at wall-thinning defect of piping components. For this purpose, a series of tensile tests was performed using several types of specimens with different stress state under tension, including smooth bars, notched round bars and grooved plates. In addition, finite element (FE) simulations were performed for all tests, and its results were compared to the test results. From the comparisons, the equivalent stress and strain corresponding to maximum load and final failure of the notched round bar specimens were proposed as the local failure criterion which is a function of stress triaxiality at notched area. The criteria were verified by employing them to the estimation of maximum load and final failure of grooved plate specimen tests.

API X65 강의 연성파괴 해석을 위한 삼축응력 영향을 고려한 파괴변형률 기준 개발

This paper presents a stress-modified fracture strain for API X65 steel used for gas pipeline, as a function of stress triaxiality. To determine the stress-modified fracture strain, tension test of bars with four different notch radii, made of API X65 steel, is firstly performed, from which true fracture strains are determined as a function of notch radius. Then detailed elastic-plastic, large strain finite element (FE) analyses are performed to estimate variations of stress triaxiality in the notched bars with load. Combining experimental with FE results provides the true fracture strain as a function of stress triaxiality, which is regarded as a criterion of ductile fracture. Application of the developed stress-modified fracture strain to failure prediction of gas pipes made of API X65 steel with various types of defects is discussed.

Fracture of 6056 aluminum sheet materials: effect of specimen thickness and hardening behavior on strain localization and toughness

The roles of specimen thickness and hardening behavior of the material on the ductile tearing resistance of a 6056 aluminum alloy are investigated separately as a function of stress triaxiality, by varying both the heat treatment (overaging or annealing + slow cooling) and the specimen geometry. The fracture path can be slanted or flat. Results show that increasing hardening capability and specimen thickness favors flat fracture. For the overaged material, the energy dissipation rate, measured on Kahn specimens, reaches a maximum value for an intermediate value of thickness (3.2 mm), whereas for the annealed material, a change in the fracture mode (from slanted to flat) induces a continuous increase in toughness with increasing thickness up to 6 mm.

Ultra high molecular weight polyethylene deformation and fracture behaviour as a function of high strain rate and triaxial state of stress

The dynamic response and fracture characteristics of Ultra High Molecular Weight Polyethylene (UHMWPE) were investigated both experimentally and numerically. The strain rate sensitivity of the material was studied by carrying out tensile tests on smooth cylindrical specimens over a range of high strain rate conditions using the purpose built `flying wedge' testing machine at separation velocities up to 9 m/s. The effect of the initial stress triaxiality conditions on the material's ductility at different strain rates was studied using pre-notched cylindrical specimens with different notch radii. The true stress-strain results indicated that the tested material is highly sensitive to strain rate changes. Post-fracture geometric measurements of the fractured specimens indicated that the ductility of UHMWPE is strongly dependent on both the initial stress triaxiality conditions and the strain rate. Numerical simulations of the quasi-static and high strain rate tests were used to predict, for different notch radii, variation of the centre-most element radial strain and stress triaxiality factor with the average radial strain. Based on the combined numerical and experimental results, a simple relation for the ductile fracture of UHMWPE was derived as a function of stress triaxiality and strain rate.

Estimation of fracture toughness transition curves of RPV steels from ball indentation and tensile test data

It was attempted to estimate the fracture toughness transition curves of reactor pressure vessel (RPV) steels from the ball indentation and tensile test data using the indentation energy to fracture (IEF) model and the relationships describing the effect of stress state on fracture. In the IEF model the fracture toughness is expressed as a function of the ball indentation test parameters and critical mean contact pressure. From the relationships among the stress components the fracture stress is derived as a function of stress triaxiality and flow property. In this approach the fracture stress calculated for the stress triaxiality of indentation deformation is assumed as the critical mean contact pressure. Indentation and tensile tests were performed on six RPV steels at transition temperatures of −160–25°C. The values of critical mean contact pressure were in the range 2500–2800 MPa. The temperature dependence of the estimated fracture toughness, K JC, agreed well with that obtained by the master curve method of ASTM E 1921 using three-point bend (TPB) specimens. In addition, the critical fracture stresses were obtained by considering the stress triaxiality for the crack tip. All test materials revealed the values of the critical fracture stress ranging from 2100 to 2500 MPa.

THE HIGH STRAIN‐RATE FRACTURE CHARACTERISTICS OF DUCTILE METALS AT ELEVATED AND SUB‐AMBIENT TEMPERATURES

Abstract— High strain‐rate tensile tests have been carried out on pre‐notched specimens of OFHC copper and Remko iron at both elevated and cryogenic temperatures. When properly expressed as a function of stress triaxiality at the centre of the notch (as predicted by numerical simulations of the experiment), the ductility of copper was found to be independent of temperature over a range from —190°C to 300°C. The specially‐processed Remko iron was found to undergo a ductile‐to‐brittle transition at a temperature dependent on the stress triaxiality and the particular batch of the material. Otherwise the fully ductile strains‐to‐failure (when expressed as a function of stress triaxiality) for iron were found to decrease with increasing temperature up to 400°C; this being the maximum temperature tested.

A new failure criterion for the Gurson-Tvergaard dilational constitutive model

In the Gurson-Tvergaard model a failure criterion has to be used to signify the void coalescence. In the literature, a constant critical void volume fraction criterion has been widely used. However, it is questionable whether the critical void volume fraction is a material constant and, furthermore, it is also difficult in practice to determine the ‘constant’. By modifying Thomason's plastic limit-load model, a new failure criterion which is fully compatible with the Gurson-Tvergaard model, is presented in this study. In the present criterion, the void coalescence failure mechanism by internal necking has been considered and the material failure is a natural result of the development of dual constitutive, stable and unstable, responses. In practical application of the present criterion, no critical void volume fraction needs to be pre-determined either numerically or experimentally. Furthermore, according to the new criterion, the void volume fraction corresponding to void coalescence is not a material constant, rather a function of stress triaxiality. The predictions using the present criterion have been compared with the finite element results by Koplik and Needleman, and very good agreement is observed. The potential advantage of this criterion and other related issues are discussed.

Investigations concerning quantitative determination of local damage in ductile materials

Ductile fracture of metallic materials can be described by void nucleation, growth and coalescence. The first coalescence of voids defines crack initiation. A quantitative description of material damage by the means of continuum‐mechanics is a very current theme. Using Gurson's model and the yield equation modified by Needleman and Tvergaard a quantitative description of damage condition is possible by connecting stress triaxiality and void volume fraction. In this paper failure curves, in which the effective plastic strain is plotted as a function of stress triaxiality, will be generated by a new yield equation, which is a further development of the Gurson model. The failure curves will be shown for crack initiation and other damage situations. An advantage of the further developed yield equation, compared with the conventional one, can be seen in the fact that not one constant, which is independent of the material, but several material specific values are used. These values can be determined by density measurements at different void volume fractions. The procedure for determination of failure curves will be shown and subsequently test results will be discussed.

Void growth and constitutive softening in a periodically voided solid

A three-dimensional finite element model of a periodically voided elastic-plastic solid is used to predict void growth and constitutive softening under tensile plastic deformation. The analysis considers an infinite block of material containing a three-dimensional periodic array of voids, subjected to a remote deformation or stress field. The predicted initial dilatational and extensional void growth rate, as a function of stress triaxiality and material work-hardening rate, agrees well with the analytical results of Budiansky et al. ( Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, edited by H.G. H opkins and M.J. Sewell, p. 13, Pergamon Press, Oxford, 1982) for an isolated void in a viscous solid. Increased initial void volume fraction (⨍) has little effect on the dilatational growth rate, but strongly affects the extensional growth rate at high levels of triaxiality. The effect of void aspect ratio on void growth rate was seen during uniaxial tensile deformation, during which extensive void elongation caused a reduction in the final or asymptotic void growth rates. Constitutive softening is shown to be primarily a function of porosity and stress triaxiality.