Ductile fracture prediction of HPDC aluminum alloy based on a shear-modified GTN damage model

Ductile fracture prediction of HPDC aluminum alloy based on a shear-modified GTN damage model

Author links open overlay panelYongfa Zhang ab, Jiang Zheng cd, Fuhui Shen b, Dongsong Li b, Sebastian Münstermann b, Weijian Han e, Shiyao Huang e, Tianjiao Li cShow moreAdd to MendeleyShareCite

https://doi.org/10.1016/j.engfracmech.2023.109541Get rights and content


In this paper, we investigate how the shear-modified Gurson-Tvergaard-Needleman (GTN) model can be used to reveal the effect of manufacturing-process-induced porosity on the scatter of ductile fracture properties of a high-pressure die-casting aluminum alloy. The GTN model exhibits great advantages in predicting the variation of failure strain/displacement by altering the initial void volume fraction (f0), compared with uncoupled ductile damage models. For a specific metallic material, one unique set of model parameters is usually determined from experiments, which leads to the fact that only a deterministic failure strain/displacement can be obtained under a fixed porosity. To overcome this shortcoming of the shear-modified GTN model, a novel parameter calibration scheme is proposed and validated in the present study. Following the physical background of the GTN model, the twelve material parameters of the shear-modified GTN model have been determined based on a combination of macroscopic mechanical tests covering a wide range of stress states and micromechanics-based unit cell simulations. Different from the existing calibration strategies, the simulation results of unit cells embedded with a spherical void have revealed a mutual dependence between the f0 and critical void volume fraction (fc). By conducting interrupted shear tests, the evolution of secondary nucleated void volume fraction was identified according to the statistical results of the fractured brittle silicon particles. The remaining parameters have been further iteratively determined. In the end, the effectiveness of the proposed parameter determination approach is confirmed based on the accurate prediction of stochastic ductile failure properties (both the global failure displacements and the local failure patterns) in different fracture tests. Given the proposed parameters identification strategy, the GTN material models have been enriched to predict the ductile failure behavior of metallic materials, which possess relatively high porosities and more pronounced scattering in failure properties.

본 논문에서는 전단 변형 Gurson-Tvergaard-Needleman(GTN) 모델을 사용하여 고압 다이캐스팅 알루미늄의 연성 파괴 특성 분산에 대한 제조 공정으로 인한 다공성의 영향을 밝히는 방법을 조사합니다.

합금. GTN 모델은 결합되지 않은 연성 손상 모델과 비교하여 초기 공극 부피 비율(f0)을 변경하여 파손 변형률/변위의 변화를 예측하는 데 큰 이점을 나타냅니다. 특정 금속 재료의 경우 일반적으로 하나의 고유한 모델 매개변수 세트가 실험을 통해 결정되며, 이는 고정된 다공성 하에서 결정론적인 파손 변형률/변위만 얻을 수 있다는 사실로 이어집니다.

전단 변형 GTN 모델의 이러한 단점을 극복하기 위해 본 연구에서는 새로운 매개변수 보정 방식을 제안하고 검증했습니다. GTN 모델의 물리적 배경에 따라 전단 변형 GTN 모델의 12개 재료 매개변수는 광범위한 응력 상태를 포괄하는 거시적 기계적 테스트와 미세 역학 기반 단위 셀 시뮬레이션의 조합을 기반으로 결정되었습니다. 기

존 보정 전략과 달리 구형 공극이 내장된 단위 셀의 시뮬레이션 결과는 f0와 임계 공극 부피 비율(fc) 사이의 상호 의존성을 나타냅니다. 단속 전단 시험을 수행함으로써 부서진 취성 실리콘 입자의 통계적 결과에 따라 2차 핵생성 공극 부피 분율의 변화가 확인되었습니다.

나머지 매개변수는 추가로 반복적으로 결정되었습니다. 결국, 다양한 파괴 시험에서 확률론적 연성 파괴 특성(전역적 파괴 변위 및 국부적 파괴 패턴 모두)의 정확한 예측을 기반으로 제안된 매개변수 결정 접근법의 효율성이 확인되었습니다.

제안된 매개변수 식별 전략을 고려하여 GTN 재료 모델은 상대적으로 높은 다공성과 파손 특성의 더 뚜렷한 산란을 갖는 금속 재료의 연성 파손 거동을 예측하기 위해 강화되었습니다.


High pressure die-casting (HPDC) is a large-scale production method with excellent production efficiency and manufacturing accuracy for aluminum alloys. Casting process parameters control the formation of initial microstructure and defects. Thereby, the mechanical properties of the fabricated component have notable effects on their structural integrity. Despite the fact that continuous efforts have been made to optimize the current casting parameters or promote the emergence of more advanced casting crafts to meet demanding performance requirements, the generation of internal voids is inevitable yet [1]. It is well-known that casting defects are always regarded as the most critical factor that facilitates early strain/stress concentration and further fracture [2]. Previous studies that considered initial voids to evaluate the plasticity of the porous metal structure are categorized into experimental statistics and numerical simulation approaches. Compared with the experimental approach that quantitatively establishes the relationship between the pore characteristics (pore size, pore location, pore density) and the performance of materials in tensile tests [3], [4], the numerical simulation approach based on material constitutive models can provide better understanding of the effects of initial voids on the failure mechanisms of the investigated material.

Depending on the interactions between damage and deformation behavior, ductile damage mechanics models are divided into two categories: uncoupled and coupled [5]. Uncoupled models employ non-porous plasticity and a fracture indicator framework, measuring the materials’ relative loss of ductility. Ductile fracture initiation is assumed to take place when a scalar variable, known as a fracture indicator, reaches a threshold value. The central concept is that the ductile fracture indicator evolves with the increasing plastic strain, which is commonly estimated through a stress-state dependent function. Due to the fact that stress triaxiality and Lode angle parameter show significant effects on the ductile fracture of metals, the stress-state dependent ductile fracture criteria have been established in the space of stress triaxiality, Lode angle parameter, and plastic strain [6], [7]. Plenty of classic uncoupled damage mechanics models, i.e., Modified Mohr-Coulomb (MMC) [8], Hosford–Coulomb (HC) [9], Bai-Wierzbicki (BW) [10], etc., have been put forward for modeling ductile fracture of metals. With the advantages of simple numerical implementation and straightforward model calibration procedure, extensive studies have been successfully carried out using uncoupled models to accurately predict the onset of ductile fracture within various types of advanced high-strength steels and aluminum alloys [11], [12], [13], [14], [15], [16], [17], [18]. As the mechanical properties of common ductile metals are analogous owing to their relatively homogeneous microstructures and low degree of existing defects, marginal variation of fracture strain/displacement is usually observed under specific loading conditions [19]. However, one of the fracture features of the investigated HPDC aluminum casting is that it exhibits large scatter in the fracture strain/displacement [20]. Recently, Zhang et al. [21] have developed a probabilistic uncoupled ductile damage model to predict the stochastic ductile fracture properties of casting alloys. Despite the fact that the macroscopic stochastic ductile fracture properties can be captured, the effects of existing defects on the evolution of damage and failure mechanisms are not considered in the developed probabilistic uncoupled approaches.

Considering the shortage of weak linkage with microscopic damage mechanisms in uncoupled fracture models, it is also necessary to explore the applicability of damage mechanism informed Gurson–Tvergaard–Needleman (GTN) in predicting stochastic ductile fracture properties. Noell et al. [22] have reported that there are several different failure mechanisms (intervoid necking, intervoid shearing, void sheeting, the Orowan alternating slip mechanism, single-plane catastrophic shear et al.), as well as their distinct interactions in the ductile rupture of metallic materials with high purity. A very comprehensive summary on the void nucleation in metals is provided in a review paper by Noell et al. [23]. For engineering structural metals and alloys used in this study, void nucleation, growth, and coalescence is recognized as the most common failure mechanism in tension-dominant loading conditions. The GTN model, as one of the most famous coupled damage models, has been broadly used to predict the ductile fracture of various metals, including steel [24], aluminum alloy [25], Ti alloy [26], etc. There are two major obstacles that restrict further applications of the GTN model: (1) the basic version of the GTN model is unable to give accurate results when fracture mode is driven by shear mechanism under low-stress triaxiality, whose applicability is also limited for anisotropic materials; (2) Too many model parameters need to be determined, and there is no universal calibration method that can be applied for all kinds of materials. Numerous scholars have made modifications to consider shear damage in the GTN model to solve the first issue. The shear enhancement is proposed mainly by adding an extra shear damage contribution factor on the growth rate of void volume fraction [27], [28], [29]. The are still intensive research activities to gain more understandings of ductile fracture using different versions of GTN models [30]. For example, Shahzamanian et al. [31] have applied the shear-modified GTN models, considering shear decohesion as an increment in the total void volume fraction, to reveal the superimposed hydrostatic pressure effect on the ductility of round-bar specimens. It is found that the shear void volume fraction at the specimen edge is increased by the superimposed hydrostatic pressure, as the stress state varies across the section of round-bar specimens. Therefore, to enhance the prediction capability of GTN models for a wide range of loading conditions, it is still necessary to perform more detailed analysis of local stress fields, as the local stress triaxiality in samples’ gauge sections ranges from the local compression state to the local biaxial tension state even in simple uniaxial tension specimens [21]. Moreover, several modified versions of the GTN model have been proposed to describe the ductile fracture of anisotropic materials [32], [33], [34], [35]. Shahzamanian et al. [33] have applied Hill’s quadratic yield criterion and defined an effective anisotropic coefficient to forecast the plastic and damage responses of anisotropic aluminum sheets. For the second issue, it is known that the identification of model parameters solely from experimental characterization is a complicated and time-consuming procedure [36]. The use of the artificial intelligence (AI) technique, as a novel predictive tool combined with the calibration process, could give users the possibility of making the best fitting and several options [37], [38]. Even though the AI strategy could provide a satisfactory approximation of the fracture behavior, the parameters in the GTN model might already lose their original physical meaning.

Finally, to the best of the authors’ knowledge, we believe there is another shortcoming of the GTN model, which only considers the initial volume fraction f0 while other void-related features (i.e., void distribution, void morphology, etc.) are not fully captured. According to the GTN model, deterministic and consistent results of fracture strain/displacements are predicted when one set of parameters is applied. However, the reality is that under the same initial void volume fraction, a pronounced scatter has been observed in the tensile ductility of some alloys due to local variations of defect (e.g., void) features [39], [40]. Therefore, it is important to further extend the applicability of the GTN models to predict the ductile fracture of metallic materials with relatively high degrees of initial defects and microstructural heterogeneity. In the meantime, a reasonable and efficient parameters determination strategy shall be provided and validated.

The present work investigates ductile damage of the porous HPDC Aural2 alloy over a broad range of stress states from both microscopic (voids growth) and macroscopic (load–displacement curves in facture tests) aspects. The shear-modified GTN model and the strategy for parameter identification, including microstructure characterization, mechanical tests, statistical analysis, and finite element simulations, are then elucidated in detail. The parameters calibration process is based on X-ray tomography measurement and macroscopic tensile tests with varied loading configurations. Moreover, quasi in-situ tensile tests using shear specimens were interrupted at pre-defined stages to characterize the microstructure evolution in the critical regions in SEM. Benefiting from the convenience and accuracy of the micromechanics-based modeling, unit cell simulations are performed to probe the void growth mechanism. After determination of the shear-related damage parameters using iterative simulations, the shear-modified damage model is evaluated in terms of its prediction ability on the failure displacement of macroscopic tensile tests and realistic porous structure models. It is found that the combination of damage model parameters could estimate the onset of fracture, especially the observed scatter of global failure displacements as well as local failure patterns with fairly well precision, which demonstrates the effectiveness and robustness of the suggested methodology of extending the applicability of GTN models to more heterogenous metallic materials.

Section snippets

Basic GTN damage model

Porous plasticity models are based on micromechanical behavior of voids with applied stress fields. Gurson [41] applied homogenization methods to study the behavior of one internal spherical void in a spherical matrix and used the damage variable f, defined as the ratio of the volume fraction of the idealized void and matrix volume in a flow potential.Φ=(����)2+2�cosh32����-(1+�2)≤0where Φ is the yield function, �� is the von Mises equivalent stress, �� is the hydrostatic stress, �� is the

Material, experimental tests and FE models

The investigated material is a high-pressure die-casting aluminum alloy (Aural-2). The chemical composition of HPDC Aural-2 is listed in Table 1. The addition of Si is used for improving castability, while Mg was added for reinforcing the alloy by generating Mg2Si precipitates. Mn in casting Al-alloys effectively increases plasticity by the formation of intermetallic compound showing needle-like and plate-like morphology that is, however, susceptible to causing brittle failure [56]. The Aural-2 

CT measurement of initial void volume fraction (f0)

In order to quantify the initial void volume fraction f0 in the studied material, X-ray computed tomography (CT) measurements on the gauge sections (29 * 6.5 * 2.5 mm3) of six different smooth dog bone specimens were performed in the present study. Raw CT data was processed and visualized with the VGStudio Max 3.2 software. The spatial distribution of internal porosity can be quantitatively displayed in 3D as shown in Fig. 5 for each individual specimen. The strain at the fracture moment of

Model validation and application

Owing to the inhomogeneous spatial distribution of microstructure (internal voids and Si particles) features, the mechanical behavior of the investigated material, particularly failure displacement/strain shows pronounced scatter in specimens produced even with the same casting parameters, as reported in [20], [75]. To ensure safe engineering applications of aluminum castings, it is necessary to predict and control the variation of failure displacement and the exact location of fracture. In


In this study, the mechanical and failure behavior of the porous HPDC Aural2 alloy were predicted using the shear-modified GTN model. Following the proposed calibration strategy presented in Section 2.3, both macroscopic mechanical tests and microscopic microstructure characterization and modeling were carried out to determine model parameters. The main purpose of this study is to extend the applicability of GTN model to describe stochastic ductile fracture properties of different porous

CRediT authorship contribution statement

Yongfa Zhang: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Jiang Zheng: Writing – review & editing, Supervision, Resources, Funding acquisition. Fuhui Shen: Writing – review & editing, Validation, Supervision, Resources. Dongsong Li: Resources, Methodology. Sebastian Münstermann: Writing – review & editing, Supervision, Resources, Funding acquisition. Weijian Han:

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


The first author (Yongfa Zhang) would like to acknowledge the financial support of the China Scholarship Council (CSC). Simulations were performed with computing resources granted by RWTH Aachen University under projects and . This study was financially co-supported by the National Natural Science Foundation of China (Nos. 51501023 and 51575068), the National Key Research and Development Program of China (No. 2016YFB0701204), Chongqing Natural Science Foundation (No. 

References (81)

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