Anisotropic ductile fracture criterion based on linear transformation

Lou, Yanshan,Yoon, Jeong Whan Elsevier 2017 International journal of plasticity Vol.93 No.-

<P><B>Abstract</B></P> <P>An anisotropic ductile fracture criterion is proposed for ductile fracture of lightweight metals. The ductile fracture criterion couples effect of stress triaxiality on void growth, and assumes the shear linking-up of voids governed by the largest shear stress. The criterion is developed based on an isotropic strain rate potential computed from an isotropic damage equivalent strain rate vector, which is mapped from the plastic strain rate vector by a forth order linear transformation tensor. The proposed anisotropic ductile fracture criterion is applied to depict anisotropic ductile fracture of AA 6K21 in shear, uniaxial tension and plane strain tension along different loading directions, and the balanced biaxial tension. The predicted fracture strain and fracture locus are compared with experimental results for the verification of the proposed criterion. The comparison demonstrates that the ductile fracture criterion properly models the anisotropy in ductile fracture under shear, uniaxial tension, plane strain tension and balanced biaxial tension with high accuracy. It shows that the proposed anisotropic ductile fracture criterion can be utilized to predict the onset of ductile fracture in plastic deformation and metal forming of lightweight metals with approximately proportional loading.</P> <P><B>Highlights</B></P> <P> <UL> <LI> An anisotropic ductile fracture criterion is newly proposed based linear transformation. </LI> <LI> Strain-rate potential is introduced to calibrate the anisotropic fracture. </LI> <LI> Tests are conducted in shear, uniaxial tension and plane strain tension along RD, DD and TD, and balanced biaxial tension. </LI> <LI> The criterion can model fracture in shear, uniaxial and plane strain tension of RD, DD and TD and balanced biaxial tension. </LI> </UL> </P>

Modeling of ductile fracture from shear to balanced biaxial tension for sheet metals

Lou, Y.,Chen, L.,Clausmeyer, T.,Tekkaya, A.E.,Yoon, J.W. Pergamon Press ; Elsevier Science Ltd 2017 International journal of solids and structures Vol.112 No.-

<P>A ductile fracture model is proposed to describe shear fracture of sheet metals from shear to balanced biaxial tension via uniaxial and plane strain tension. The fracture criterion models plastic damage as strain-induced void nucleation, triaxiality-governed void enlargement, Lode-controlled void torsion, and shear-restrained coalescence of voids. Its flexibility is investigated by a parameter study of the ductile fracture model proposed. The fracture model is employed to describe ductile fracture behavior of an aluminum alloy AA6082 T6 (thickness: 1.0 mm). Dogbone specimens are strained to characterize the strain hardening properties, while another four different specimens are tested to characterize fracture behavior in shear, uniaxial tension, plane strain tension and balanced biaxial tension. The loading processes are analyzed numerically with the stress invariant-based Drucker yield function which is for the first time specified for body-centered cubic and face-centered cubic metals. Fracture strains in various loading conditions are measured with a hybrid experimental-numerical approach. The measured fracture strains are then used to calibrate the ductile fracture model proposed. The ductile fracture model calibrated above is employed to predict the onset of ductile fracture for these four specimens. For the purpose of comparison, the predicted fracture strokes of these four loading conditions are compared with those predicted by the modified Mohr-Coulomb model (Bai and Wierzbicki, 2008), and two micromechanism-inspired criteria proposed recently (Lou et al., 2012, 2014). The comparison reveals that the proposed model predicts the fracture behavior in much better agreement compared with experimental results from shear to the balanced biaxial tension. Accordingly, the proposed ductile fracture criterion is recommended for the prediction of ductile fracture in sheet metal forming processes, optimization of forming parameters and design of tools for both solid elements and shell elements. Besides, the ductile fracture model proposed can also be applied in various bulk metal forming processes in case that the model is calibrated by proper sets of experiments. (C) 2017 Elsevier Ltd. All rights reserved.</P>

고강도강판에서의 전단파단

박근환(Keunhwan Pack),안광현(Kwanghyun Ahn),허훈(Hoon Huh) 한국자동차공학회 2011 한국자동차공학회 학술대회 및 전시회 Vol.2011 No.11

Substituting advanced high strength steels (AHSS) for existing mild steels to enhance crashworthiness and fuel efficiency gives rise to new types of fracture so-called ‘shear fracture’ during forming process due to their reduced ductility. However, the term, ‘shear fracture’, is used in various cases because there is no specific definition of it. Shear fracture in AHSS can be classified into two types. The first type is observed at die radius when sheets are stamped with small R / t ratio (ratio of die radius to sheet thickness). The second type is in-plane shear fracture where the main fracture mechanism is in-plane shear deformation. In this paper, before everything, the term, ‘shear fracture’, is defined for four cases. The stretch-bending test at quasi-static state is simulated with Abaqus/Explicit based on the experimental conditions1) for various R / t values to identify the first type. Deformation process is analyzed to explain the transition of fracture type and load-displacement curves obtained from the simulation are compared with that of the experiment to secure validity of the simulation. Furthermore, strain paths of various material points are investigated in the square-cup-drawing process to identify the second type of shear fracture.

Effect of shear-span/depth ratio on cohesive crack and double-K fracture parameters of concrete

Choubey, Rajendra Kumar,Kumar, Shailendra,Rao, M.C. Techno-Press 2014 Advances in concrete construction Vol.2 No.3

A numerical study of the influence of shear-span/depth ratio on the cohesive crack fracture parameters and double - K fracture parameters of concrete is carried out in this paper. For the study the standard bending specimen geometry loaded with four point bending test is used. For four point loading, the shear - span/depth ratio is varied as 0.4, 1 and 1.75 and the ao/D ratio is varied from 0.2, 0.3 and 0.4 for laboratory specimens having size range from 100 - 500 mm. The input parameters for determining the double - K fracture parameters are taken from the developed fictitious crack model. It is found that the cohesive crack fracture parameters are independent of shear-span/depth ratio. Further, the unstable fracture toughness of double-K fracture model is independent of shear-span/depth ratio whereas, the initial cracking toughness of the material is dependent on the shear-span/depth ratio.

2행 1열 오스테나이트계 스테인리스강(STS304) 볼트접합부의 종전단 및 블록전단 파단내력에 관한 조사

조영준(Jo, Young-Jun),김태수(Kim, Tae-Soo) 대한건축학회 2023 대한건축학회논문집 Vol.39 No.12

This study investigates the fracture patterns and ultimate strengths of the double shear two-bolted connections made of austenitic stainless steel STS304, which is widely used in building structures. The main variables include the plate thickness and end distance in the loading direction. A total of 10 test specimens were planned and fabricated. For specimens with relatively short end distance of less than 24mm, shear-out fractures occurred, while, specimens with end distances of 36mm or more showed typical block shear fracture mode. The strengths of both domestic and international design codes (KDS, AISC, AISI, ASCE, AIJ and EC3) and the equations of shear-out and block shear fractures proposed by the previous researcher were compared with test results. The current standards underestimated the test strengths of double shear two-bolted connections of austenitic stainless steel, and shear-out fracture and block shear fracture equations suggested by other researchers based on carbon steel or duplex stainless steel bolted connections were found to provide good predictions.

산청 회장암복합체 내 발달하는 단열계의 기하학적·운동학적 특성

이덕선(Deok-Seon Lee),강지훈(Ji-Hoon Kang) 한국암석학회 2016 암석학회지 Vol.25 No.4

영남육괴 지리산지구의 남동부에 위치하는 산청지역은 주로 선캄브리아시대 지리산 변성암복합체, 산청 회장암복합체, 중생대 화성암류 등으로 구성되어 있다. 산청 회장암복합체 내에는 다수의 단열조의 상대적인 시간관계(선후관계 및 공존관계)와 전단단열의 발달순서 및 운동감각을 결정하는데 이용되는 기하학적 지시자가 잘 관찰된다. 본 논문은 이들 다수의 단열조에 대한 방향성과 운동학적·기하학적 특성을 정밀하게 분석하여 산청 회장암복합체에 발달하는 인장단열의 발달순서와 전단단열의 발달순서 및 운동성을 고찰하였다. 그 결과 산청 회장암복합체에 발달하는 단열계는 적어도 5회의 변형단계(Dn 단계에서 Dn+3 이후단계로 명기)를 걸쳐 형성되었음이 인지된다. (1) Dn 단계: 북북서-남남동 방향의 인장단열 형성기. 이후 응력장 변화로 인해 우수향 → 좌수향 전단단열운동을 활동하였다. (2) Dn+1 단계: (북)북동-(남)남서 방향의 인장단열 형성기. 이 단계의 단열조는 이후 좌수향 → 좌수향 → 우수향 전단단열운동으로 재활동하였다. (3) Dn+2 단계: 북서-남동 방향의 인장단열 형성기. 이후, 우수향 전단단열운동을 겪었다. (4) Dn+3 단계: 남-북 방향의 인장단열 형성기. (5) Dn+3 이후단계: (동)북동-(서)남서 방향의 인장단열 형성기. Dn 단계는 송림조산운동 전기, Dn+1 단계는 송림조산운동 후기, Dn+2 단계는 대보조산운동 시기, Dn+3 단계는 불국사 조산운동 시기 그리고 Dn+3 이후단계는 불국사 조산운동 시기 이후에 형성되었다. The study area, which is located in the southeastern part of the Jirisan province of the Yeongnam massif, Korea, consists mainly of the Precambrian Sancheong anorthosite complex and the Jirisan metamorphic rock complex, the Mesozoic granitoids which intruded them. Several fracture sets with various geometric indicators, which determine their relative timing and shear sense, are well observed in the Sancheong anorthosite complex. The aim of this study is to determine the development sequence of extension fractures, the movement sense and development sequence of shear fractures in the Sancheong anorthosite complex on the basis of detailed analysis of their geometric indicators. This study suggests fracture system of the Sancheong anorthosite complex was formed at least through five different fracturing events, named as Dn to Post-Dn+3 phases. (1) Dn phase: extension fracturing event of NNW trend. The fracture set experienced the reactivations of dextral → sinistral shearing with the change of stress field afterward. (2) Dn+1 phase: extension fracturing event of (N)NE trend. The fracture set experienced the reactivations of sinistral → sinistral → dextral. (3) Dn+2 phase: extension fracturing event of NW trend. The fracture set experienced the activated of dextral shearing. (4) Dn+3 phase: extension fracturing event of N-S trend. (5) Post-Dn+3 phase: extension fracturing event of (E)NE trend. Dn deformation formed during the early Songnim orogeny. Dn+1 deformation formed during the late Songnim orogeny. Dn+2 deformation formed during the Daebo orogeny. Dn+3 deformation formed during the Bulguksa orogeny.

경상분지 의성지괴 길안면지역에서 청송화강암의 단열 발달사 및 운동성에 대한 기하학적 해석

강지훈(Ji-Hoon Kang),류충렬(Chung-Ryul Ryoo) 한국암석학회 2006 암석학회지 Vol.15 No.4

경상분지 의성지괴의 중앙 북부에 위치하는 안동시 길안면 지역은 선캠브리아기 변성암류, 트라이아스기 청송화강암, 백악기 초 하양층군, 백악기 말-고제3기 화성암류 등으로 구성되어 있다. 이 지역에는 다양한 방향의 단층(남북 내지 북북서 방향의 옥산단층, 북서 방향의 길안단층, 서북서 방향의 황학산단층, 그리고 동서 방향의 임봉산단층)들이 발달하고, 경상분지의 기반암류에 해당하는 청송화강암내에는 다수 단열조의 상대적 시간관계(선후관계 및 공존관계)와 전단단열의 운동감각을 결정하는데 이용되는 기하학적 지시자가 잘 관찰된다. 본 논문은 이들 단열조의 기하학적 특성(연결, 종료, 교차형상 및 절단관계)에 대한 정밀한 분석을 통하여 경상분지 의성지괴 길안면 지역에 발달하는 인장단열의 발달사와 전단단열의 운동성을 연구하였다. 그 결과, 길안면 지역에 발달하는 단열계는 적어도 7회의 변형단계(Dn 이전 단계에서 Dn+5 단계로 명기)를 걸쳐 형성되었고, 단열조의 우세 방향성은 길안면 주변지역에 발달하는 지질도 규모의 단층 우세 방향성과 거의 일치하는 (서)북서, 북북서, 북북동, 동서, 북동 순서로 나타난다. 단열조의 발달사와 운동성를 요약하면 다음과 같다. (1) Dn 이전 단계: 남북 내지 북북서 또는 서북서 내지 동북동 방향의 인장단열 형성기. 이후 응력장 변화와 함께 남북 내지 북북서 방향의 절리조는 좌수향→우수향→좌수향 전단단열운동으로 그리고 서북서 내지 동북동 방향의 절리조는 (우수향→) 좌수향 전단단열운동으로 각각 재활동하였다. (2) Dn 단계: 북서 방향의 인장단열 형성기. 이 단계의 절리조는 이후 좌수향→우수향 순서의 전단단열운동을 경험한다. (3) Dn + 1 단계: 북북동 내지 북동 방향의 인장단열 형성기. 이후, 좌수향 전단단열운동으로 활동하게 된다. (4) Dn+2 단계: 동북동 내지 동서 방향의 인장단열 형성기. (5) Dn + 3 단계: 서북서 내지 북서 방향의 인장단열 형성기. (6) Dn+4 단계: 북북서 방향의 인장단열 형성기. 이후, 우수향 전단단열운동으로 활동하였다. (7) Dn + 5 단계: 북북동 방향의 인장단열 형성기. The Gilan area in the central-northern part of Uiseong Block of Cretaceous Gyeongsang Basin is composed of Precambrian metamorphic rocks, Triassic Cheongsong granite, Early Cretaceous Hayang Group, and Late Cretaceous-Paleocene igneous rocks. In this area, the faults of various directions are developed: Oksan fault of NS-NNW trend, Gilan fault of NW trend, Hwanghaksan fault of WNW trend, and Imbongsan fault of EW trend. Several fracture sets with various geometric indicators, which determine their relative timing (sequence and coexistence relationships) and shear sense, are well observed in the Cheongsong granite, the basement of Gyeongsang Basin. The aim of this study is to determine the development sequence of extension fractures and the movement sense of shear fractures in the Gilan area on the basis of detailed analysis of their geometric indicators (connection, termination, intersection patterns, and cross-cutting relations). This study suggests that the fracture system of the Gilan area was formed at least through seven different fracturing events, named as Pre-Dn to Dn + 5 phases. The orientations of fracture sets show (W) NW, NNW, NNE, EW, NE in descending order of frequency. The orientation and frequency patterns are concordant with those of faults around and in the Gilan area on a geological map scale. The development sequence and movement sense of fracture sets are summarized as follows. (1) Pre-Dn phase: extension fracturing event of NS-NNW and/or WNW-ENE trends. The joint sets of NS-NNW trend and of WNW-ENE trend underwent the reactivation histories of sinistral→ dextral→ sinistral shearing and of (dextral→) sinistral shearing with the change of stress field afterward, respectively. (2) Dn phase: that of NW trend. The joint set experienced the reactivations of sinistral → dextral shearing. (3) Dn + 1 phase: that of NNE-NE trend. The joint set was reactivated as a sinistral shear fracture afterward. (4) Dn + 2 phase: that of ENE-EW trend. (5) Dn + 3 phase: that of WNW-NW trend. (6) Dn + 4 phase: that of NNW trend. The joint set underwent a dextral shearing after this. (7) The last Dn + 5 phase: that of NNE trend.

Numerical Analysis of AHSS Fracture in a Stretch-bending Test

Meng Luo,Xiaoming Chen,Ming F. Shi,Hua-Chu Shih 한국소성가공학회 2010 기타자료 Vol.2010 No.6

Advanced High Strength Steels (AHSS) are increasingly used in the automotive industry due to their superior strength and substantial weight reduction advantage. However, their limited ductility gives rise to numerous manufacturing issues. One of them is the so-called ‘shear fracture’ often observed on tight radii during stamping processes. Since traditional approaches, such as the Forming Limit Diagram (FLD), are unable to predict this type of fracture, efforts have been made to develop failure criteria that can predict shear fractures. In this paper, a recently developed Modified Mohr-Coulomb (MMC) ductile fracture criterion[1] is adopted to analyze the failure behavior of a Dual Phase (DP) steel sheet during stretch bending operations. The plasticity and ductile fracture of the present sheet are fully characterized by the Hill’48 orthotropic model and the MMC fracture model respectively. Finite Element models with three different element types (3D, shell and plane strain) were built for a Stretch Forming Simulator (SFS) test and numerical simulations with four different R/t ratios (die radius normalized by sheet thickness) were performed. It has been shown that the 3D and shell element models can accurately predict the failure location/mode, the upper die loaddisplacement responses as well as the wall stress and wrap angle at the onset of fracture for all R/t ratios. Furthermore, a series of parametric studies were conducted on the 3D element model, and the effects of tension level (clamping distance) and tooling friction on the failure modes/locations were investigated.

Sn-Ag-Cu-In 4원계 무연솔더 조인트의 고속 전단 특성

김주형,현창용,Kim, Ju-Hyung,Hyun, Chang-Yong 한국마이크로전자및패키징학회 2014 마이크로전자 및 패키징학회지 Vol.21 No.2

본 연구에서는 고속 전단시험의 변형속도를 500 mm/s로 설정한 상태에서 Sn-Ag-Cu계(Sn-1.0wt.%Ag-0.5Cu 및 Sn-4.0Ag-0.5Cu)뿐만이 아니라 4종의 4원계 Sn-Ag-Cu-In 조성(Sn-1.0Ag-0.5Cu-1.0In, Sn-1.2Ag-0.5Cu-0.4In, Sn-1.2Ag-0.5Cu-0.6In, Sn-1.2Ag-0.7Cu-0.4In)을 포함하는 무연 솔더 접합부의 솔더링 직후 및 시효 시간에 따른 파면 생성결과, 접합강도 및 접합부 파괴에너지값의 변화를 측정, 비교해 보았다. 그 결과, 리플로우 솔더링 직후 및 $125^{\circ}C$에서의 500 시간 시효까지 주로 연성 파괴모드 및 준연성 파괴모드가 관찰되었으며, 준연성 파괴모드의 발생 빈도를 분석할 때 고속 전단조건에서 상용 무연 솔더 조성인 Sn-3.0Ag-0.5Cu 이상의 연성파괴 특성을 나타내는 것으로 파악되었다. 또한 4원계 무연 솔더 조인트는 평균적으로 Sn-Ag-Cu계 조성 수준의 파단에너지값을 나타내었는데, 약 100 시간의 시효 후 최고의 파단에너지값이 관찰되었으나 500 시간의 시효 후에는 파단에너지값의 확연한 감소가 관찰되어 500 시간의 시효시점부터 솔더 접합 계면부의 신뢰성 감소가 가속화되는 경향을 관찰할 수 있었다. With Pb-free solder joints containing Sn-Ag-Cu-based ternary alloys (Sn-1.0 wt.%Ag-0.5Cu and Sn-4.0Ag-0.5Cu) and Sn-Ag-Cu-In-based quaternary alloys (Sn-1.0Ag-0.5Cu-1.0In, Sn-1.2Ag-0.5Cu-0.4In, Sn-1.2Ag-0.5Cu-0.6In, and Sn-1.2Ag-0.7Cu-0.4In), fracture-mode change, shear strengths, and fracture energies were observed and measured under a high-speed shear test of 500 mm/s. The samples in each composition were prepared with as-reflowed ones or solid-aged ones at $125^{\circ}C$ to 500 h. As a result, it was observed that ductile or quasi-ductile fracture modes occurs in the most of Sn-Ag-Cu-In samples. The happening frequency of a quasi-ductile fracture mode showed that the Sn-Ag-Cu-In joints possessed ductile fracture properties more than that of Sn-3.0Ag-0.5Cu in the high-speed shear condition. Moreover, the Sn-Ag-Cu-In joints presented averagely fracture energies similar to those of Sn-Ag-Cu joints. While maximum values in the fracture energies were measured after the solid aging for 100 h, clear decreases in the fracture energies were observed after the solid aging for 500 h. This result indicated that reliability degradation of the Sn-Ag-Cu-In solder joints might accelerate from about that time.

Sn-Ag-Cu-In 4원계 무연솔더 조인트의 고속 전단 특성

김주형,현창용 한국마이크로전자및패키징학회 2014 마이크로전자 및 패키징학회지 Vol.20 No.2

본 연구에서는 고속 전단시험의 변형속도를 500 mm/s로 설정한 상태에서 Sn-Ag-Cu계(Sn-1.0wt.%Ag-0.5Cu및 Sn-4.0Ag-0.5Cu)뿐만이 아니라 4종의 4원계 Sn-Ag-Cu-In 조성(Sn-1.0Ag-0.5Cu-1.0In, Sn-1.2Ag-0.5Cu-0.4In, Sn-1.2Ag-0.5Cu-0.6In, Sn-1.2Ag-0.7Cu-0.4In)을 포함하는 무연 솔더 접합부의 솔더링 직후 및 시효 시간에 따른 파면 생성결과, 접합강도 및 접합부 파괴에너지값의 변화를 측정, 비교해 보았다. 그 결과, 리플로우 솔더링 직후 및 125oC에서의500 시간 시효까지 주로 연성 파괴모드 및 준연성 파괴모드가 관찰되었으며, 준연성 파괴모드의 발생 빈도를 분석할 때고속 전단조건에서 상용 무연 솔더 조성인 Sn-3.0Ag-0.5Cu 이상의 연성파괴 특성을 나타내는 것으로 파악되었다. 또한4원계 무연 솔더 조인트는 평균적으로 Sn-Ag-Cu계 조성 수준의 파단에너지값을 나타내었는데, 약 100 시간의 시효 후최고의 파단에너지값이 관찰되었으나 500 시간의 시효 후에는 파단에너지값의 확연한 감소가 관찰되어 500 시간의 시효시점부터 솔더 접합 계면부의 신뢰성 감소가 가속화되는 경향을 관찰할 수 있었다. With Pb-free solder joints containing Sn-Ag-Cu-based ternary alloys (Sn-1.0 wt.%Ag-0.5Cu and Sn-4.0Ag-0.5Cu) and Sn-Ag-Cu-In-based quaternary alloys (Sn-1.0Ag-0.5Cu-1.0In, Sn-1.2Ag-0.5Cu-0.4In, Sn-1.2Ag-0.5Cu-0.6In,and Sn-1.2Ag-0.7Cu-0.4In), fracture-mode change, shear strengths, and fracture energies were observed and measuredunder a high-speed shear test of 500 mm/s. The samples in each composition were prepared with as-reflowed ones orsolid-aged ones at 125oC to 500 h. As a result, it was observed that ductile or quasi-ductile fracture modes occurs in themost of Sn-Ag-Cu-In samples. The happening frequency of a quasi-ductile fracture mode showed that the Sn-Ag-Cu-Injoints possessed ductile fracture properties more than that of Sn-3.0Ag-0.5Cu in the high-speed shear condition. Moreover,the Sn-Ag-Cu-In joints presented averagely fracture energies similar to those of Sn-Ag-Cu joints. While maximum valuesin the fracture energies were measured after the solid aging for 100 h, clear decreases in the fracture energies were observedafter the solid aging for 500 h. This result indicated that reliability degradation of the Sn-Ag-Cu-In solder joints mightaccelerate from about that time.