Effect Of Stress Triaxiality Research Articles

On the ductile rupture of 13% Cr-4% Ni martensitic stainless steels

Ductile rupture of 13% Cr-4% Ni martensitic stainless steels was examined during tension testing in order to better understand the role of second phase particles in these materials. SEM fracture surface examinations revealed that micro-voids were initiated from inclusions, and these inclusions were characterized from metallographic polished sections. Effect of stress triaxiality on the growth and impingement of the micro-voids were examined using a modified model of Rice and Tracey. In the case of the cast and wrought versions, the true fracture strains predicted for the measured stress triaxiality values were in a good agreement with the measured ones. For the weld metals, only the contribution of the micro-void growth cannot explain the experimental results, and it shows that the matrix properties such as austenite content and hardness of martensite play a significant contribution. The magnitude of the final stress triaxiality ratio measured after rupture was also related to the inclusion characteristics.

Prediction of ductile fracture for circular hollow section bracing members under extremely low cycle fatigue

The fracture behaviour of concentrically loaded circular hollow section (CHS) bracing members under extremely low cycle fatigue (ELCF) is examined in this paper. Finite element (FE) models capable of predicting fracture initiation and propagation on cyclically loaded braces were developed. A structural steel ductile fracture criterion, together with a damage accumulation rule that can account for the effects of both stress triaxiality and Lode angle, was adopted in the FE models. The FE models were validated against the available test results from different experimental programmes and shown to provide an accurate prediction of both the hysteretic response and the ELCF fracture cracking process. The coupling effects of buckling and fracture on the ELCF performance of braces were assessed through a parametric study. This parametric study examined the influences of the geometry, material and manufacturing process on the local and global deformation, and the ductility of the braces. Predictive equations for the localized strains and member ductility were proposed based on a plastic hinge model. The seismic performance of a chevron braced frame was also evaluated in terms of storey drift angle according to the requirements of the current design code.

Continuum damage mechanics modelling incorporating stress triaxiality effect on ductile damage initiation

AbstractMicromechanical modelling of void nucleation in ductile metals indicates that strain required for damage initiation reduces exponentially with increasing stress triaxiality. This feature has been incorporated in a continuum damage mechanics (CDM) model, providing a phenomenological relationship for the damage threshold strain dependence on the stress triaxiality. The main consequences of this model modification are that the failure locus is predicted to change as function of stress triaxiality sensitivity of the material damage threshold strain and that high triaxial fracture strain is expected to be even lower than the threshold strain at which the damage processes initiate at triaxiality as low as 1/3. The proposed damage model formulation has been used to predict ductile fracture in unnotched and notched bars in tension for two commercially pure α‐iron grades (Swedish and ARMCO iron). Finally, the model has been validated, predicting spall fracture in a plate‐impact experiment and confirming the capability to capture the effect of the stress state on material fracture ductility at very high stress triaxiality.

Stress triaxiality effect on void nucleation in ductile metals

AbstractThe stress triaxiality effect on the strain required for void nucleation by particle‐matrix debonding has been investigated by means of micromechanical modelling. A unit‐cell model considering an elastic spherical particle embedded in an elastic‐plastic matrix was developed to the purpose. Particle‐matrix decohesion was simulated through the progressive failure of a cohesive interface. It has been shown that the parameters of matrix‐particle cohesive interface are correlated with macroscopic material properties. Here, a simple relationship for the maximum cohesive opening at interface failure as a function of material fracture toughness and yield stress has been derived. Results seem to confirm that, increasing stress triaxiality, the strain at which void nucleation is predicted to occur decreases exponentially in a similar way as for fracture strain. This result has substantial implications in modelling of ductile damage because it indicates that if the stress triaxiality is high enough, ductile fracture can occur at plastic strain lower than that necessary to nucleate damage for moderate or low stress triaxiality regime.

Fracture of Titanium Alloys at High Strain Rates and under Stress Triaxiality

The present study investigates the effect of stress triaxiality on mechanical behavior and fracture of Ti-5Al-2.5Sn alloy in a practical relevant strain rate range from 0.1 to 1000 s−1. Tensile tests were carried out on flat smoothed and notched specimens using an Instron VHS 40/50-20 servo-hydraulic test machine. High-speed video registration was conducted by Phantom 711 Camera. Strain fields on the specimen gauge area were investigated by the digital image correlation method (DIC). The fracture surface relief was studied using digital microscope Keyence VHX-600D. Stress and strain fields during testing of the Ti-5Al-2.5Sn alloy were analyzed by the numerical simulation method. The evolution of strain fields at the investigated loading condition indicates that large plastic deformation occurs in localization bands. The alloy undergoes fracture governing by damage nucleation, growth, and coalescence in the localized plastic strain bands oriented along the maximum shear stresses. Results confirm that the fracture of near alpha titanium alloys has ductile behavior at strain rates from 0.1 to 1000 s−1, stress triaxiality parameter 0.33 < η < 0.6, and temperature close to 295 K.

Effect of stress triaxiality on the damage of polyethylene

In this study, the effect of the triaxial stress state on the stress/strain behavior and damage of polyethylene (PE) was investigated through a combination of experimental testing and finite-element (FE) simulation. Notched round bars with four different notch radii (0.5, 2, 5, and 20 mm) were stretched at a crosshead speed of 1mm/min until fracture. A phenomenological constitutive model was proposed to describe the mechanical behavior of PE specimens with different radii. Parameters of the constitutive model were adjusted until the curve of engineering stress-displacement from the FE simulation matched the experimental results. The FE model was further applied to obtain the data on stress triaxiality and true stress-strain curves of PE specimens. The results show that stress triaxiality and yield stress increase with the reduction of notch radii. However, the true stress decreases when the notch radii are reduced, suggesting that higher triaxiality aggravates the damage accumulation.

Fracture Behavior of Annealed and Equal Channel Angular Pressed Copper: An Experimental Study

In this research, the ductile fracture of ultra-fine-grained copper was investigated. Ultra-fine-grained copper was produced using equal channel angular pressing process. During this process, the average grain size of the copper specimens decreases. Experiments have shown that stress state has significant effect on fracture behavior and should be included in the constitutive models. Therefore, the ductile failure was analyzed here by focusing on its relationship with the effect of hydrostatic pressure and Lode angle parameter. Tensile tests were performed on smooth and notched round bar specimens as well as doubly grooved samples. Moreover, the fracture surfaces were investigated by a scanning electron microscope. The experimental results reveal that the stress triaxiality and Lode angle parameter have a remarkable effect on the ductile fracture of the ECAPed specimens. However, the effect of stress triaxiality on ductility reduction is more significant than the effect of the Lode angle parameter. Also, the experimental results show the transition from the tensile ductile fracture to shear fracture in the ECAPed specimens.

Experiments and numerical simulation of damage and fracture of the X0-specimen under non-proportional loading paths

The paper deals with new non-proportional biaxial experiments and corresponding numerical simulations to analyze the load-history dependence on damage and fracture behavior of ductile metals. The numerical simulations are based on a phenomenological, thermodynamically consistent anisotropic continuum damage model considering the effect of stress triaxiality and Lode parameter on damage behavior. The model as well as the corresponding material parameter identification is discussed and a full set of material parameters is given. The new biaxial experiments take into account non-proportional and corresponding proportional loading paths with special focus on stress states changes from shear to tension dominated cases. The corresponding strain fields of critical regions of the X0-specimen have been analyzed by digital image correlation technique and indicate good accordance with the numerically predicted ones. The evolution of the calculated plastic and damage fields elucidate the relevance of both independent mechanisms. The results are supported by scanning electron microscopy images of the fracture surfaces. This experimental–numerical technique applied to the non-proportional biaxial experiments provides new insights of the stress and load-history dependent damage and fracture processes.

Effect Of Stress Triaxiality On The Strain Concentration Factor

Axisymmetric machine element with irregularities such as notches encountered with effects of stress triaxiality on the strain concentration factor (SNCF) at the reduced section. The effect of notch geometries on the triaxial stress state development in the critical section of a notched cylindrical bar is studied here using FEM. In addition, the effect of triaxial stress state (TSS) on the SNCF is evaluated. To this end, a notched cylindrical bars with notch depths from extremely deep notch (do/Do = 0.2) shallow notch (do/Do = 0.95) has been employed. The results show that the notches introduce a TSS at the critical section, which strongly affected by the notch depth as well as the notch radii. In this paper, a new concentration factor is introduced as the ratio of the stress triaxiality factor at the notch root (TFNR) to the average triaxiality on the critical section (), i.e. the triaxiality concentration factor KTF. The numerical results reveal that the variation of the average triaxiality factor with total strain shows the same trend as that of the SNCF. The variation of the elastic values of TFCN, , , and SNCF with do/Do and show that the minimum TFNR leads to the maximum elastic SNCF. It is prominent that elastic TFNR is less that elastic TFCN for 0.2 ≤ do/Do ≤ 0.85, while it is greater for shallow notches. The current results indicate a strong compatibility between the newly defined triaxiality concentration factor and the SNCF up to general yielding.

An Investigation on Base Metal Block Shear Strength of Ferritic Stainless Steel Welded Connection

This study develops a finite element analysis model to predict the ultimate strength of the base metal block shear fracture based on previous experimental results and compares the experimental results with the analysis results to verify the effectiveness of the analysis model. This study also analyzed additional variables of the welding direction and weld length on the applied load to investigate the structural behaviors and fracture conditions. In addition, predicted strength according to the analysis results were compared with those by the current design equations, and the equations proposed by previous researchers. As a result, the design formula by the current design equations, such as Korea Building Code (KBC)/American Institute of Steel Construction (AISC) and European Code (EC3), and the equations proposed by Oosterhof and Driver underestimated the base metal block shear strength of ferritic stainless steel by up to 42%. Equations suggested by Topkaya and Lee et al. for carbon steel and austenitic stainless steel welded connections provided more accurate strength predictions, while they did not reflect the difference of material properties. Therefore, this study proposed a modified strength equation for ferritic stainless steel welded connection with base metal block shear fracture considering the stress triaxiality effect of the welded connection and the material properties of ferritic stainless steel.

Effect of Stress Triaxiality on Plastic Damage Evolution and Failure Mode for 316L Notched Specimen

To reveal the effect of stress triaxiality on plastic damage evolution and failure mode, 316L notched specimens with different notch sizes are systematically investigated by digital image correlation (DIC) observation, plastic damage analysis by finite element simulation, and void mesoscopic observation. It was found that the plastic damage evolution and failure mode are closely related with notch radius and stress triaxiality. The greater the stress triaxiality at the root is, the greater the damage value at the root is and the earlier the fracture occurs. Moreover, void distribution by mesoscopic observation agrees well with damage distribution observed by finite element simulation with the Gurson-Tvergaard-Needleman (GTN) damage model. It is worth noting that, with the increase in stress triaxiality, the failure mode of notched specimen changes from ductility fracture with void coalescence at the center position to crack initiation at the notch root, from both mesoscopic observation and damage simulation.

A reexamination of high strength steel yield criterion

The high strength steel (HSS) with a nominal yield stress not less than 460 N/mm2 has been increasingly used in engineering structures. An accurate yield criterion which describes the elastoplastic behavior of high strength steels under complex stress states, is significant for the analysis and design of high strength steel structures. For ductile metal materials, the most generally used the von Mises yield criterion neglects the effects of stress triaxiality and Lode angle on the metal plasticity. However, due to the reduce ductility with the increase in strength, such yield criterion may not applicable to HSSs. In the present paper, the tests of six types of specimens are carried out to evaluate effects of stress triaxiality and Lode angle on the plastic behavior of HSSs (Q550, Q690 and Q890). The applicability of von Mises yield criterion is examined firstly using experimental results and finite element analyses. It demonstrates that an appropriate yield function of HSSs should consider effects of the Lode angle while the influence of stress triaxiality is negligible. Based on the experimental and numerical results, a yield function for HSSs is proposed, to essentially simulate the elastoplastic behavior of high strength steel under complex stress states.

A new Dynamic Plasticity and Failure Model for Metals

A new plasticity and failure model is developed herein for metallic materials subjected to dynamic loadings on the basis of the analysis of some available material test data and previous work. The new model consists of two parts: a strength model and a failure criterion. The strength model takes into consideration both tension and shear stress-strain relationships, as well as the effect of Lode angle, while the failure criterion takes into account both the effects of stress triaxiality and Lode angle. Furthermore, the effects of strain rate and temperature are also catered for in the model. In particular, new non-linear functions are suggested for the effects of strain rate and temperature in the strength model in order to describe accurately the mechanical behavior of metallic materials at very high loading rates and temperature. The new model is compared with available material test data for 2024-T351 aluminum alloy, 6061-T6 aluminum alloy, oxygen free high conductivity (OFHC) copper, 4340 steel, Ti-6Al-4V alloys, and Q235 mild steel in terms of stress–strain curves in both tension and shear, strain rate effect, temperature effect and fracture under different loading conditions. The new model is also compared with the JC constitutive model with the respective JC and BW fracture criteria by conducting numerical simulations of quasi-static smooth and notched bar tensile tests and ballistic perforation tests on 2024-T351 aluminum alloy in terms of cup and cone failure pattern, ballistic limit, residual velocity and failure mode. It transpires that the new plasticity and failure model can be used to predict the response and failure of metallic materials and structures under different loading conditions. It also transpires that the new model is advantageous over the existing models.

The effects of stress triaxiality and strain rate on the fracture strain of Ti6Al4V

The fracture strain is known to be affected by the stress state and strain rate. To measure the fracture strain over a wide range of stress triaxiality and strain rate, a rectangular hat-shaped specimen is designed. This specimen can be tested at low rates with a conventional load frame and at high rates with a Split Hopkinson Pressure Bar (SHPB). The specimen’s flat face facilitates the use of Digital Image Correlation (DIC) technique. The fracture strain of Ti6Al4V was determined for a stress triaxiality varying from −0.31 to 0.50 at strain rates ranging from quasi-static to 103/s. The results indicate that the fracture strain decreased with increasing either the stress triaxiality or the strain rate. A fracture strain model incorporating the effects of stress triaxiality and strain rate was established.

An experimental methodology to characterise post-necking behaviour and quantify ductile damage accumulation in isotropic materials

The development of ductile damage, that occurs beyond the point of necking in a tensile test, can be difficult to quantify. An experimental methodology has been developed to accurately characterise the post-necking deformation response of a material through continuous monitoring of the specimens shape up until rupture. By studying the evolution of the neck geometry, the correct values of the local stress and strain have been determined in samples of grade 304L stainless steel and C110 copper. Notched bar specimens of various notch acuities were examined enabling the effects of stress triaxiality on ductile fracture to be determined. The methodology developed has provided a robust framework for macroscopic measurements of ductile damage during the necking process. To characterise the material degradation process, the elastic modulus reduction method was employed on hourglass-shaped specimens of the same materials. Stiffness degradation was measured using a small gauge extensometer during uninterrupted tensile tests with partial elastic unloadings. A metallographic study was conducted on progressively damaged specimens in order to validate the macroscopic damage measurements. A new non-linear ductile damage accumulation law has been developed and calibrated, which provides an advanced representation of the experimental results, and a significant improvement compared to linear accumulation models frequently employed. This realistic modelling approach considers the degradation of the material when it has undergone severe plastic deformation, and provides a more accurate representation of the near failure behaviour by considering the effects of stress triaxiality. The methodology provides accurate data for damage model development and calibration, to improve the predictions of remnant life from ductile damage in engineering components.

Plasticity Effect on the Mechanical Behavior of an Amorphous Polymer

In the process of forming solid materials, the plastic instability phenomena often control the appearance and performance of the finished product. The study of these phenomena is therefore of great scientific and technological importance. Polymers materials, for example, polyvinyl chloride (PVC) are frequently used in the plastic pipes in pressure vessels and pipelines, which require details that are more serious, it is therefore essential to understand the mechanisms of plastic instability in polymers in order to know how to control them. In order to determine the plastic behaviour of PVC, the true stress-strain response under large plastic deformation was investigated in different stress triaxiality frameworks. A particular attention was given on the volumetric strain evolution and the damage. The effect of stress triaxiality on the fracture strain was also examined. In the second part of this paper, an elasto-viscoplastic behaviour model is presented, with non associated plasticity, damage and coalescence, which represents the observed behaviours of a PVC material under different triaxialities and for three initial void shapes

Block shear strength of cold-formed austenitic stainless steel (304 type) welded connection with base metal fracture

In this paper, the block shear fracture behavior of base metal in austenitic stainless steel (STS304, corresponds to ASTM 304 type) fillet-welded connection has been investigated through experimental and numerical methods. Even though the block shear fracture strength of welded connection thanks to stress triaxiality effect differs from those of bolted connection under monotonic tension, block shear strength equations of welded connection with base metal fracture in the design codes are identical to those of bolted connection. Main variables are weld method (TIG and Arc welding) and weld length (transverse and longitudinal to the direction of loading). It is found from study results that welding method did not affect the strength of welded connection. Block shear strengths by current codes (KBC2016, AISC2016 and EC3 1–3) and other researchers’ proposed equations were compared with those of experimental results and finite element analysis results. Finite element analysis (FEA) model was developed based on previously test data. Also, parametric study for investigating the weld length effect on strength has been performed with the developed finite element analysis procedures. Consequently, condition of weld length and end distance perpendicular to the direction of applied force for fracture mode transition boundary from tensile fracture to block shear fracture in welded connection was investigated. In addition, block shear strength equation with modified tensile stress and shear stress factors of base metal fracture in austenitic stainless steel (STS304) welded connection is suggested considering stress triaxiality.

Impact resistance prediction of superalloy honeycomb using modified Johnson–Cook constitutive model and fracture criterion

In this study, to further understand the containment properties of a containment ring, the deformation behavior of GH3536 superalloy used as the material of the containment ring were investigated over a wide range of temperatures and strain rates. The effects of stress triaxiality, temperature, and strain rate on the fracture behavior of the superalloy were analyzed. According to the temperature and strain rate dependences of the deformation behavior, the original Johnson-Cook constitutive model (J––C model) was unable to describe such behavior, and a modified J–C model was developed. In view of the stress triaxiality, temperature and strain rate dependences of the fracture behavior, the original Johnson–Cook fracture criterion (J–C criterion) was inapplicable to describe such fracture behavior, and a modified J–C criterion was proposed. Finally, the impact resistance of honeycomb structure made from the superalloy and applied on the containment ring were tested at different temperatures, impact velocities and impact angles. Using the modified J–C model and J–C criterion, the resistance property of the honeycomb structure could be accurately predicted.

An improved procedure for acquiring yield curves over a large range of strains

Acquiring a full range of yield curves is a long-standing challenge in material science and engineering. Such curves are extremely important for stress analysis using finite element simulation. In this article, we proposed an improved procedure integrating finite element analysis and hybrid particle swarm optimization to extract a post-necking yield curve from a smooth tensile round bar. The investigated material was 3Cr1MoV. The strain range of the yield curve was extended from 0.0681 mm/mm before necking to 1.5 mm/mm. The results revealed that curves obtained through this procedure are reliable and unique. Three notched round bars were designed to investigate the effects of stress triaxiality on the yield curves. We found that stress triaxiality has a significant influence on curves at large plastic strains (strain > 0.3 mm/mm) and has a negligible effect at low plastic strains (strain < 0.3 mm/mm). Studies revealed that the stress triaxiality-dependent yield curves are related to dilatational plasticity arising from nucleation and growth of voids.

Simulation of ductile fracture initiation in steels using a stress triaxiality–shear stress coupled model

Micromechanics-based models provide powerful tools to predict initiation of ductile fracture in steels. A new criterion is presented herein to study the process of ductile fracture when the effects of both stress triaxiality and shear stress on void growth and coalescence are considered. Finite-element analyses of two different kinds of steel, viz. ASTM A992 and AISI 1045, were carried out to monitor the history of stress and strain states and study the methodology for determining fracture initiation. Both the new model and void growth model (VGM) were calibrated for both kinds of steel and their accuracy for predicting fracture initiation evaluated. The results indicated that both models offer good accuracy for predicting fracture of A992 steel. However, use of the VGM leads to a significant deviation for 1045 steel, while the new model presents good performance for predicting fracture over a wide range of stress triaxiality while capturing the effect of shear stress on fracture initiation.