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1

A comparative study of various models of equivalent plastic strain to fracture

Mykhalevych Volodymyr, Dobraniuk Yurii, Matviichuk Victor, Kraievskyi Volodymyr, Тiutiunnyk Oksana, Smailova Saule, Kozbakova Ainur

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2023

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T. 13, nr 1

64--70

EN

For more then half a centre just the same approach to the simulation of the ductile crack formation wasdeveloped independently by the scientific communities of foreign and native researchers. The importance at these studies drastically increased. A set of the characteristics, according to whichit is recommendly to perform thedetail comparison of the existing fracture models is developed. The examples of the analysis of a number of the most popular models by means of obtaining and study their analytical expressions regarding the conditions of the plane state are given. The generalized relations of the know models and a number of separate relations are obtained.

PL

Od ponad pół wieku to samo podejście do modelowania uszkodzeń podczas odkształceńplastycznych jest opracowywane niezależnie przez zespoły naukowe złożone znaukowców zagranicznych i krajowych. W ostatnich dziesięcioleciach znaczenie tych badań dramatycznie wzrosło. Opracowano zestaw cech, zgodnie z którymi proponuje się przeprowadzenie szczegółowego porównania istniejących modeli zniszczenia. Podano przykłady analizy szeregu najpopularniejszych modeli poprzez uzyskanie i badanie ich wyrażeń analitycznych dla warunków płaskiego stanunaprężenia. Otrzymano uogólnione wskaźniki znanych modeli oraz szereg wskaźników indywidualnych.

2

AA5052 failure prediction of electromagnetic flanging process using a combined fracture model

Deng Huakun, Mao Yunfei, Li Guangyao, Zhang Xu, Cui Junjia

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e84, 1--17

EN

Electromagnetic forming process could significantly increase the forming limit of aluminum alloy. However, high-speed fracture prediction of aluminum alloys is a major problem in the development of electromagnetic flanging process. In this study, notched specimen tensile tests with high-speed Digital Image Correlation system were conducted under the strain rate range from 0.001 to 100 s-1. A fracture model of AA5052 alloys which combined of an uncoupled fracture model, Gissmo damage evolution model and Johnson-Cook strain rate effect was established. Electromagnetic flanging experiments were conducted to verify the failure criteria effectiveness. Results showed that failure strain was significantly influenced by strain rate under various loading path. Compared with the experiments, the percentage error of established electromagnetic flanging process FEM model was less than 4%. The fracture model established could well predict notched specimen high-speed failure, and also accurately predict sheet failure model of electromagnetic flanging experiments and, thus, verified the effectiveness of the established dynamic failure criteria in electromagnetic flanging process.

3

Experimental and numerical investigation on plasticity and fracture behaviors of aluminum alloy 6061-T6 extrusions

Zhu Peihua, Zhang Qilin, Xu Hongjun, Ouyang Yuanwen

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 3

13--30

EN

Aluminum alloy 6061-T6 (AA 6061-T6) extrusions have been widely applied in large-span reticulated shells. However, researches on behaviors of the aluminum alloy under large deformation and fracture by means of meso-mechanics are still insufficient. This paper focuses on the plastic and fracture behaviors of AA 6061-T6 extrusions over a wide range of stress states. Experiments on smooth and notched round bars, grooved plates and shear plates are conducted. It is observed that the yield stress decreases as the notch or groove radius decreases. The yield stress under plane strain or pure shear is lower than that under axisymmetric tension. In addition, true stress–true strain data obtained from tensile coupon tests overestimate the hardening behavior at large deformation. To fully describe these experimental observations, a new plastic model considering the pressure dependence, Lode angle effect, and hardening with post-necking correction is proposed. Regarding the ductile fracture, modified Mohr–Coulomb fracture model with damage-induced softening is adopted to predict crack initiation and propagation under different stress states. The material models of plasticity and fracture are numerically implemented into FE code ABAQUS/explicit by the material subroutine VUMAT. It is found that both the overall nominal stress–strain curves and fracture patterns for all specimens are well predicted by the material models. For practical engineering design, recommended reduced values of shear strength and high-triaxiality tensile strength of AA 6061-T6 extrusions are given.

4

Application of two fracture models in impact simulations

Fras T., Roth C. C., Mohr D.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 2

317--325

EN

The following discussion concerns modelling of fracture in steel plates during an impact test, in which both target and striker are manufactured from the same material, high-strength high-hardness armour steel – Mars® 300. The test conditions (3 mm thick targets, projectiles with different nose shapes at impact velocity lower than 400 m/s) result in severely damaged components, which results in an analysis of stress states showing material failure. Numerical analyses are performed using two material models: the Johnson-Cook approach, as traditionally used in impact simulations, accounting for the effect of stress triaxiality, strain rate and temperature and for comparison, a simulation by means of the stress triaxiality and Lode angle parameter-dependent Hosford-Coulomb model, also incorporating the effect of the strain rate on a fracture initiation. The aim of the study is to analyse the mechanisms of penetration and perforation observed in the armour steel plates and validation of the modelling approaches.

5

Protocol to define material behaviour and failure strain level at low and high strain rates based on a compression test

Jankowiak T., Rusinek A., Bendarma A.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 2

471--481

EN

Compression test is frequently used to define material behaviour. However, this test may be depending on different effects, for example friction, specimen inertia or local stress triaxiality. For this reason, a new design is proposed to analyse the previous effects and to try to minimize it on quantities measured as macroscopic stress and strain. To have a complete understanding, numerical simulations have been performed using finite element method (Abaqus/Standard and Abaqus/Explicit). It allows one to define the macroscopic behaviour and to have an access to the local values not accessible during experiments for a better understanding of the experimental measurements.

6

Analysis of the void volume fraction for S235JR steel at failure for low initial stress triaxiality

Kossakowski P. G.

Archives of Civil Engineering

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2018

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Vol. 64, nr 1

101--115

EN

This paper deals with problems of failure mechanisms of S235JR structural steel. One of the fundamental parameters of the Gurson-Tvergaard-Needleman damage mechanics-based material model is considered in order to describe the behaviour of the material at the plastic range. The analysis was performed on the void volume fraction fF determined at failure of S235JR steel. The case of low initial stress triaxiality η = 1/3 was taken into consideration. Different from the most popular methods such as curve-fitting, the experimental method based on the digital image analysis of the fracture surface of S235JR steel is proposed in order to determine the critical parameter fF.

PL

Tematem pracy są zagadnienia związane z mechanizmami towarzyszącymi procesowi niszczenia stali konstrukcyjnej S235JR. Zakres badań obejmował końcową fazę uplastycznienia materiału, aż do momentu jego zniszczenia. W przeprowadzonej analizie oparto się na podejściu mechaniki zniszczenia, wykorzystując model materiału porowatego Gursona-Tvergaarda-Needlemana (GTN). Zbadano jeden z podstawowych parametrów mikrostruktury GTN, krytyczny udział objętościowy pustek fF. Współczynnik ten determinuje proces niszczenia materiału od chwili wzrostu i łączenia się mikrodefektów struktury materiałowej, aż do dekohezji materiału w skali makro. Badania przeprowadzono dla przypadku niskiego wstępnego stopnia trójosiowości naprężeńη = 1/3. W odróżnieniu od najpopularniejszych metod, takich jak np. procedura dopasowania parametrów analizy do krzywych wzorcowych, zaproponowano metodę eksperymentalną, opartą na analizie rzeczywistych obrazów powierzchni pęknięć stali S235JR uzyskanych doświadczalnie. Cyfrowa analiza obrazowa powierzchni pęknięć pozwoliła na określenie wartości udziału objętościowego pustek fF w momencie zniszczenia materiału, co umożliwiło eksperymentalne wyznaczenie krytycznego parametru fF dla stali S235JR. W pracy przedstawiono również wyniki analizy numerycznej, weryfikującej rezultaty uzyskane w badaniach doświadczalnych. Symulowano przypadek rozciągania statycznego elementu o przekroju kołowym, który modelowano przy zastosowaniu modelu materiału GTN. Wyznaczone wartości parametru fF pozwoliły na symulację procesu uplastycznienia stali S235JR oraz przewidzenie momentu jej zniszczenia.

7

Damage characterization of aluminum 2024 thin sheet for different stress triaxialities

Majzoobi G. H., Kashfi M., Bonora N., Iannitti G., Ruggiero A., Khademi E.

Archives of Civil and Mechanical Engineering

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2018

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Vol. 18, no. 3

702--712

EN

Due to its attractive mechanical properties, aluminum 2024 is widely used in aircraft manufacturing industries, especially as fiber metal laminates, such as GLARE. In the present work, a series of experiments for different stress triaxialities are used to study the ductile damage of Al 2024 considering continuum damage mechanics (CDM). Stress triaxiality is produced using notched specimens. The main objective of the present study is to predict the local equivalent plastic strain to fracture and introducing a relation which describes the effect of stress triaxiality factor (TF) on it in the medium range of stress triaxiality. Hence, a nonlinear damage model is utilized for Al 2024 and its parameters are determined by an experimental/numerical/optimization procedure using tensile test on plain specimens. The experiments showed that for large notch specimens (Al-NL) and medium notch samples (Al-NM) fracture started from the center of the notch root of the specimens, whereas for small notched specimens (Al-NS) the failure initiated from the notch root surface. Finite element simulations are performed using the presented nonlinear damage model and are compared with the experimental data. Results show that the proposed damage model can predict the damage evolution for different stress triaxialities.

8

Calibration of constitutive equations under conditions of large strains and stress triaxiality

Neimitz A., Galkiewicz J., Dzioba I.

Archives of Civil and Mechanical Engineering

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2018

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Vol. 18, no. 4

1123--1135

EN

Constitutive equations were calibrated to improve their application in assessing a stress field in front of a crack under the conditions of large strains and stress triaxiality. The Bai–Wierzbicki method was adopted, and certain changes and new terms were introduced to incorporate material softening. Five shapes of specimens were tested to cover a wide range of stress triaxiality conditions and Lode factors. Tests were performed at three different temperatures, namely, +20 °C, –20 °C, and –50 °C, and on three different materials obtained by three different heat treatments of S355JR steel.

9

Influence of Failure Strain of Different Aluminium Alloys on Dynamic Problems

Rodriguez-Millan M., Vaz-Romero A., Rodriguez-Martinez J. A., Rusinek A., Arias A.

Engineering Transactions

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2012

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Vol. 60, iss. 4

345-353

EN

In this work an experimental-numerical methodology is devised for analyzing ductile frac- ture of two aluminum alloys under different values of stress triaxiality (0:2 1:2) and Lode parameter ( 1 0). The experiments developed include combined loading (tension- torsion) tests on same NT specimen geometry for A 5754-H111 and AA 6082-T6. Numerical analysis shows that this type of specimen exhibits uniformity stable values of stress triaxiality and Lode parameter as plastic strain develops. Experimental results can be used to compare failure strain corresponding to different stress states. Moreover, to consider the influence of stress state in failure mechanics under impact loads, perforation tests of aluminum alloys have been developed in a range of impact velocity between 120 v 500 m/s. The tests were carried out with three di?erent shape projectiles: conical (m = 29:4 g) and two blunt ones (m = 29:4 g and m = 1:1 g). Results show the dependence on energy absorption with stress state and failure strain.

10

State of stress identification in numerical modeling of 3D issues

Kut S.

Archives of Metallurgy and Materials

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2009

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Vol. 54, iss. 3

627-632

EN

The purpose of the stress triaxiality k is an unequivocal identification via single numerical value of the state of stress in the point (FEM node) for individual shaping process phases. The paper presents the analysis of the stress triaxiality k both for planar and tree-dimensional cases. The imperfections of currently used stress triaxiality k have been indicated and a new factor kn had been proposed. This new factor unequivocally allows to determine the state of stress both for 2D (two-dimensional) and 3D (three-dimensional) problems.

PL

W mechaniczno-matematycznym podejściu do modelowania odkształcenie i pękanie materiału silnie zależy od stanu naprężenia panującego w kształtowanym materiale. Praktyczne zastosowanie funkcji odkształcalności granicznej, czy też znanych z literatury licznych kryteriów do prognozowania pekania materiału w procesach technologicznych, wiąże się z koniecznością jednoznacznego określenia stanu naprężenia panującego w poszczególnych obszarach kształtowanego materiału. Posługiwanie się w takich przypadkach tensorem naprężenia jest niepraktyczne i trudne. Z tego względu stan naprężenia obecnie najczęściej opisuje się za pomocą wskaźnika stanu naprężenia stanowiącego stosunek naprężeń średnich do intensywności naprężeń. Zadaniem wskaźnika stanu naprężenia k jest za pomocą jednej wartości liczbowej jednoznacznie identyfikowac stan naprężenia w punkcie (węźle – MES) na poszczególnych etapach procesu kształtowania. W pracy przeprowadzono analizę wskaźnika stanu naprężenia k zarówno dla przypadków rozważanych jako płaskie jak i przestrzenne. Wskazano na niedoskonałości obecnie stosowanego wskaźnika k i zaproponowano nowy wskaźnik kn, pozwalający jednoznacznie określić stan naprężenia zarówno w modelowaniu zagadnień płaskich 2-D jak i przestrzennych 3-D. Jego praktyczne zastosowanie w modelowaniu numerycznym procesów plastycznego kształtowania materiałów wiaze sie jedynie z koniecznością napisania prostego podprogramu działajacego według przedstawionego w pracy algorytmu.

11

Ductile fracture locus of AC4CH-T6 cast aluminium alloy

Mae H., Teng X., Bai Y., Wierzbicki T.

Archives of Computational Materials Science and Surface Engineering

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2009

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Vol. 1, nr 2

100-105

EN

Purpose: Cast aluminium alloys have found wide application to manufacture lighted-weight components of complex shape in automotive and aerospace industries. To improve the strength and ductility of cast aluminium alloys, it is necessary to study their fracture properties by conducting a series of tests. This study addresses calibration of ductile fracture property of the cast aluminium alloy (AC4CH-T6) made by the gravity die casting with sand mold. Design/methodology/approach: 6 round bar specimens and 6 butterfly specimens are machined from the actual cast component. The tensile tests on the smooth and notched round bar specimens are performed to calibrate the fracture strain in the range of high positive stress triaxialities. The combined loading tests on the butterfly specimens are carried out using a uniquely designed Universal Biaxial Testing Device (UBTD). These tests cover the fracture properties in the rage of low and negative stress triaxialities. Detailed finite element models of all the tests are developed. The fracture locus in the space of the effective plastic strain to fracture and the stress triaxiality are constructed in a wide rage from -1/3 to 1.0. Findings: It is found that material ductility sharply decreases with the stress triaxiality. The material ductility at the negative stress triaxiality is much higher than that in the positive stress triaxiality. Research limitations/implications: Large spread of data is observed for those tests repeated on the same loading configuration, necessitating the statistical analysis of the fracture processes. Practical implications: It is expected that such a fracture criterion would be able to correctly predict the fracture response of actual cast aluminum components under complex loading in the practical applications. Originality/value: The conventional researches focused on the material ductility at the stress triaxiality larger than +1/3. The present study showed the material ductility at the wide range of stress triaxiality from -1/3 to 1.0.