scholarly journals Stress Triaxiality and Lode Angle Parameter Characterization of Flat Metal Specimen with Inclined Notch

Metals ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1627
Author(s):  
Jian Peng ◽  
Peishuang Zhou ◽  
Ying Wang ◽  
Qiao Dai ◽  
David Knowles ◽  
...  
Keyword(s):  
Stress State ◽  
Notch Root ◽  
Stress Triaxiality ◽  
Image Correlation ◽  
Notch Angle ◽  
Strain Evolution ◽  
Metal Specimen ◽  
Lode Angle ◽  
Stress States ◽  
Angle Parameter

The stress state has an important effect on the deformation and failure of metals. While the stress states of the axisymmetric notched bars specimens are studied in the literature, the studies on the flat metal specimen with inclined notch are very limited and the stress state is not clearly characterized in them. In this paper, digital image correlation and finite element simulations are used to study the distribution of strain and stress state, that is stress triaxiality and Lode angle parameter. Flat specimen with inclined notch was tested to extract the full field strain evolution and calculate stress state parameters at three locations: specimen centre, notch root and failure starting point. It is found that compared with the centre point and the notch root, the failure initiation point can better characterize the influence of the notch angle on the strain evolution. Conversely, the centre point can more clearly characterize the effect of the notch angle on stress state, since the stress states at the failure point and the notch root change greatly during the plastic deformation. Then the calculated stress state parameters of the flat metal specimen with inclined notch at the centre point are used in Wierzbicki stress state diagram to establish a relationship between failure mode and stress state.

scholarly journals Effect of Stress Triaxiality on the Strain Concentration Factor

2019 ◽  
Vol 8 (4) ◽  
pp. 3468-3474
Keyword(s):  
Stress State ◽  
Concentration Factor ◽  
Notch Root ◽  
Stress Triaxiality ◽  
Critical Section ◽  
Triaxial Stress ◽  
Triaxial Stress State ◽  
Strain Concentration ◽  
Machine Element ◽  
Triaxiality 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.

On the Application of Stress Triaxiality Formula for Plane Strain Fracture Testing

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Yuanli Bai ◽  
Xiaoqing Teng ◽  
Tomasz Wierzbicki
Keyword(s):  
Closed Form ◽  
Plane Strain ◽  
Fracture Strain ◽  
Closed Form Solution ◽  
Stress Triaxiality ◽  
Form Solution ◽  
Fracture Locus ◽  
Strain Fracture ◽  
Lode Angle ◽  
Angle Parameter

Theoretical and experimental studies have shown that stress triaxiality is the key parameter controlling the magnitude of the fracture strain. Smooth and notched round bar specimens are mostly often used to quantify the effect of stress triaxiality on ductile fracture strain. There is a mounting evidence (Bai and Wierzbicki, 2008, “A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence,” Int. J. Plast., 24(6), pp. 1071–1096) that, in addition to the stress triaxiality, the normalized third deviatoric stress invariant (equivalent to the Lode angle parameter) should also be included in characterization of ductile fracture. The calibration using round notched bars covers only a small range of possible stress states. Plane strain fracture tests provide additional important data. Following Bridgman’s stress analysis inside the necking of a plane strain specimen, a closed-form solution is derived for the stress triaxiality inside the notch of a flat-grooved plane strain specimen. The newly derived formula is verified by finite element simulations. The range of stress triaxiality in round notched bars and flat-grooved specimens is similar, but the values of the Lode angle parameter are different. These two groups of tests are therefore very useful in constructing a general 3D fracture locus. The results of experiments and numerical simulations on 1045 and DH36 steels have proved the applicability of the closed-form solution and have demonstrated the effect of the Lode angle parameter on the fracture locus.

scholarly journals On Phenomenological Failure Loci of Metals under Constant Stress States of Combined Tension and Shear: Issues of Coaxiality and Non-Uniqueness

Metals ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 1052
Author(s):  
Cliff Butcher ◽  
Armin Abedini
Keyword(s):  
Stress State ◽  
Plane Stress ◽  
Simple Shear ◽  
Stress Triaxiality ◽  
Failure Surface ◽  
Equivalent Strain ◽  
Shear Loading ◽  
Stress Conditions ◽  
Failure Locus ◽  
Stress States

The present study investigates how the choice of characterization test and the composition of the stress state in terms of tension and shear can produce a non-unique failure locus in terms of stress triaxiality under plane stress conditions. Stress states that are composed of tensile and simple shear loadings result in a loss of proportionality between the cumulative strain and stress such that the principal frames become non-coaxial despite a constant stress triaxiality. Consequently, it is shown that the conventional interpretation of a failure locus in plane stress is based upon an implicit assumption of proportional coaxial loading. The use of simple shear tests along with traditional in-plane tensile tests for fracture characterization is only one “path” that can be taken in terms of the stress triaxiality, which may produce a bifurcation at uniaxial tension while the tension–torsion path does not. In general, the failure locus in terms of the equivalent strain is a failure surface and must consider the composition of the stress state that produces a given triaxiality. A comprehensive review of phenomenological fracture loci within a modified Mohr-Coulomb (MMC) framework is performed to highlight how the choice of stress states obtained using different characterization tests can change the apparent fracture locus of a material. The finite strain solutions for the work conjugate equivalent strain are derived for various loading paths that produce the same stress triaxiality. It is then shown that accounting for non-coaxiality leads to equivalent failure strains that are even higher than previously reported in tension–torsion tests within the literature. The equivalent plastic strains integrated from finite-element simulations are work-conjugate by definition. The equivalent strains estimated from the cumulative principal strains using DIC strain measurement depend upon a coaxial or non-coaxial assumption. Finally, an analytical solution for the onset of diffuse necking that accounts for the stabilizing influence of shear loading against a tensile instability is considered. Even under plane stress conditions, a failure surface arises in terms of the equivalent strain at necking, the stress triaxiality, and the severity of shear loading.

Ductile Fracture Prediction for Marine Structures

2015 ◽  
Author(s):  
Pawel B. Woelke ◽  
Badri Hiriyur ◽  
Brett Benowitz ◽  
John W. Hutchinson
Keyword(s):  
Stress Triaxiality ◽  
Experimental Tests ◽  
Calibration Procedure ◽  
Damage Evolution Equation ◽  
Shell Elements ◽  
Third Invariant ◽  
Lode Angle ◽  
Stress States ◽  
Constitutive Formulation ◽  
Structural Scale

Reliable modelling of fracture on a structural scale restricts the type of the finite elements used in the analyses to shell elements with in-plane dimension larger than the thickness. Thus, we consider a comprehensive constitutive formulation embedded in the shell mechanics framework. We propose a three-invariant plasticity model that accounts for dependence of the strain at fracture on both stress triaxiality and the third invariant of the deviatoric stress, which has a significant influence for shear-dominated stress states. This is achieved through a phenomenological damage evolution equation that includes both the dilatational term and plastic deviatoric energy term. The latter is dependent on the omega parameter, which can be considered a normalization of the Lode angle. A consistent calibration procedure is also developed based on a small number of carefully selected coupon-level experimental tests.

scholarly journals Experimental investigation of strain rate dependent damage mechanisms in DP1000 automotive steel

2021 ◽  
Vol 250 ◽  
pp. 03005
Author(s):  
Sarath Chandran ◽  
Patricia Verleysen
Keyword(s):  
Stress State ◽  
Strain Rate ◽  
Local Strain ◽  
Image Correlation ◽  
Plane Shear ◽  
Damage Mechanisms ◽  
Rate Dependent ◽  
Series Of Experiments ◽  
Stress States ◽  
Automotive Steel

Present study aims to investigate the effect of stress state and loading rates on the damage mechanisms in a DP1000 steel using a welldesigned series of experiments. A specimen family comprising of central hole, in-plane shear and plane strain samples is applied to characterise damage under well-controlled stress states. The optimization of the specimen geometries is achieved using finite element simulations. To assess the influence of strain rate, quasi-static, intermediate and dynamic tests are performed on the designed samples. Local strain fields are obtained by digital image correlation. After testing, scanning electron microscopy is employed to systematically analyse the micromechanisms driving the damage in the investigated material. The underlying damage mechanisms are ferrite-martensite interphase debonding, martensite cracking and debonding at ferrite-ferrite grain boundaries. Stress state and strain rate are found to have distinct influences on triggering the underlying damage mechanisms.

On the Development and Identification of Phenomenological Damage Models - Application to Industrial Wire Drawing and Rolling Processes

2013 ◽  
Vol 554-557 ◽  
pp. 213-226 ◽  
Author(s):  
Trong Son Cao ◽  
Christian Bobadilla ◽  
Pierre Montmitonnet ◽  
Pierre Olivier Bouchard
Keyword(s):  
Stress Tensor ◽  
Damage Model ◽  
Stress Triaxiality ◽  
Wire Drawing ◽  
Damage Models ◽  
The Third ◽  
Third Stress Invariant ◽  
Lode Angle ◽  
Stress Invariant ◽  
Angle Parameter

The continuum thermodynamics-based Lemaitre damage model is nowadays widely used to deal with coupled damage analyses for various mechanical applications (e.g. forming process simulations). However, such a model, which only accounts for the stress triaxiality (the ratio between the first and the second invariants of stress tensor) has been found to give incorrect results under shear dominated loading (in terms of damage location as well as risk of crack). Several recent studies have demonstrated the importance of the third stress invariant in damage prediction; the Lode angle parameter is generally used to include it. The idea is to describe completely the stress state in damage model’s formulations, which is defined by the equivalent stress, the stress triaxiality ratio and the Lode angle parameter. This later parameter has proved to have an important influence on ductile damage under low stress triaxiality. Xue’s coupled damage model accounts for the third invariant of the deviatoric stress tensor, allowing a better balance between respective effects of shear and elongation on damage. Some extensions of more physically based damage models, such as the Gurson-Tvergaard-Needleman model, have also been presented to account for this influence of the third stress invariant. In the present work, the phenomenological damage models have been implemented in Forge® Finite Element (FE) software to investigate ductile damage occurring during industrial forming processes. This paper presents the comparative study of Xue’s model and Lemaitre’s model. A complete procedure is detailed to identify the material and damage parameters from experimental mechanical tests on high carbon steel. This identification process has been carried out both for Lemaitre’s coupled damage model and Xue’s coupled damage model. Application to wire drawing followed by flat rolling shows that in such shear-inducing processes, these models predict damage at different locations, due to their different emphasis on shear with respect to elongational strain damage.

Short Stress State Questionnaire

2015 ◽  
Vol 31 (1) ◽  
pp. 20-30 ◽  
Author(s):  
William S. Helton ◽  
Katharina Näswall
Keyword(s):  
Stress State ◽  
Factor Structure ◽  
Human Performance ◽  
Self Report ◽  
Confirmatory Factor ◽  
Stress States ◽  
Related Stress ◽  
Using Data ◽  
Task Conditions ◽  
Multiple Samples

Conscious appraisals of stress, or stress states, are an important aspect of human performance. This article presents evidence supporting the validity and measurement characteristics of a short multidimensional self-report measure of stress state, the Short Stress State Questionnaire (SSSQ; Helton, 2004 ). The SSSQ measures task engagement, distress, and worry. A confirmatory factor analysis of the SSSQ using data pooled from multiple samples suggests the SSSQ does have a three factor structure and post-task changes are not due to changes in factor structure, but to mean level changes (state changes). In addition, the SSSQ demonstrates sensitivity to task stressors in line with hypotheses. Different task conditions elicited unique patterns of stress state on the three factors of the SSSQ in line with prior predictions. The 24-item SSSQ is a valid measure of stress state which may be useful to researchers interested in conscious appraisals of task-related stress.

scholarly journals A Study of Yielding and Plasticity of Rapid Prototyped ABS

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1495
Author(s):  
Dan-Andrei Șerban ◽  
Cosmin Marșavina ◽  
Alexandru Viorel Coșa ◽  
George Belgiu ◽  
Radu Negru
Keyword(s):  
Experimental Data ◽  
Stress State ◽  
Plastic Flow ◽  
Plane Stress ◽  
Yield Criterion ◽  
Numerical Analyses ◽  
Flow Potential ◽  
Stress States ◽  
State Configuration

In this article, the yielding and plastic flow of a rapid-prototyped ABS compound was investigated for various plane stress states. The experimental procedures consisted of multiaxial tests performed on an Arcan device on specimens manufactured through photopolymerization. Numerical analyses were employed in order to determine the yield points for each stress state configuration. The results were used for the calibration of the Hosford yield criterion and flow potential. Numerical analyses performed on identical specimen models and test configurations yielded results that are in accordance with the experimental data.

scholarly journals Use of the AE Effect to Determine the Stresses State in AAC Masonry Walls under Compression

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3459
Author(s):  
Radosław Jasiński ◽  
Krzysztof Stebel ◽  
Paweł Kielan
Keyword(s):  
Ultrasonic Waves ◽  
Image Correlation ◽  
Masonry Walls ◽  
Acceptable Error ◽  
Compressive Stresses ◽  
Deformation State ◽  
Hydrostatic Stresses ◽  
Stress States ◽  
The Impact ◽  
Masonry Units

Safety and reliability of constructions operated are predicted using the known mechanical properties of materials and geometry of cross-sections, and also the known internal forces. The extensometry technique (electro-resistant tensometers, wire gauges, sensor systems) is a common method applied under laboratory conditions to determine the deformation state of a material. The construction sector rarely uses ultrasonic extensometry with the acoustoelastic (AE) method which is based on the relation between the direction of ultrasonic waves and the direction of normal stresses. It is generally used to identify stress states of machine or vehicles parts, mainly made of steel, characterized by high homogeneity and a lack of inherent internal defects. The AE effect was detected in autoclaved aerated concrete (AAC), which is usually used in masonry units. The acoustoelastic effect was used in the tests described to identify the complex stress state in masonry walls (masonry units) made of AAC. At first, the relationships were determined for mean hydrostatic stresses P and mean compressive stresses σ3 with relation to velocities of the longitudinal ultrasonic wave cp. These stresses were used to determine stresses σ3. The discrete approach was used which consists in analyzing single masonry units. Changes in velocity of longitudinal waves were identified at a test stand to control the stress states of an element tested by the digital image correlation (DIC) technique. The analyses involved density and the impact of moisture content of AAC. Then, the method was verified on nine walls subjected to axial compression and the model was validated with the FEM micromodel. It was demonstrated that mean compressive stresses σ3 and hydrostatic stresses, which were determined for the masonry using the method considered, could be determined even up to ca. 75% of failure stresses at the acceptable error level of 15%. Stresses σ1 parallel to bed joints were calculated using the known mean hydrostatic stresses and mean compressive stresses σ3.

An Experimental Measurement of Toughness Locus for a Ductile Material

2005 ◽  
Vol 297-300 ◽  
pp. 2410-2415 ◽  
Author(s):  
Dong Hak Kim ◽  
Jeong Hyun Lee ◽  
Ho Dong Kim ◽  
Ki Ju Kang
Keyword(s):  
Crack Length ◽  
Nuclear Power ◽  
Power Plants ◽  
Test Procedure ◽  
Stress Triaxiality ◽  
Crack Tip ◽  
Potential Drop ◽  
Image Correlation ◽  
Ductile Material ◽  
Main Steam

A toughness locus Jc-Q for a ductile steel, SA106 Grade C used in the main steam piping of nuclear power plants, has been experimentally evaluated. Along with the standard fracture test procedure for J-R curve, Q as the second parameter governing stress triaxiality nearby the crack tip is measured from the displacements nearby the side necking which occurs near the crack tip on the lateral surface of a fracture specimen. The displacements nearby the side necking are measured from the digital images taken during the fracture experiment based on Stereoscopic Digital Photography (SDP) and high resolution Digital Image Correlation (DIC) software. The crack length is monitored by Direct Current Potential Drop (DCPD) method and the J-R curve is determined according to ASTM standard E1737-96. The effects of crack length, specimen geometry and thickness of specimen are studied, which are included in the toughness locus Jc-Q.

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