Constitutive prediction of the defect susceptibility of tensile properties to microporosity variation in A356 aluminum alloy

Abstract

The aim of this study is to verify the physical meaning of the defect susceptibility of tensile properties to microporosity variation in terms of the constitutive law for tensile deformation. Additionally, it aims to investigate the contributions of plastic constraint factors describing the geometric array of eutectic Si particles and micro-voids as well as of strain-related factors to the defect susceptibility of tensile properties through theoretical prediction and systematic experiments on T4-treated A356 alloy. The empirical relationship proposed in previous studies to describe defect susceptibility can be theoretically described in terms of the constitutive law, which takes into account the strain-hardening exponent, strain rate sensitivity and microporosity terms. The modified constitutive model can very accurately predict the defect susceptibility of tensile elongation, far more accurately than the original Ghosh model. The strain-hardening exponent has practical significance, affecting the defect susceptibility of tensile elongation to microporosity variation because of its additional contribution to the plastic constraint factor, whereas the strain rate sensitivity has a minor effect on the variation of defect susceptibility. The plastic constraint factor of eutectic Si particles has a relatively lower contribution to the defect susceptibility than the plastic constraint factor of micro-voids, rather slightly increasing the defect susceptibility by increasing the maximum elongation in the defect-free condition.

Introduction

Aluminium alloys have been identified as potential materials enabling efficient weight reduction in the automobile and aerospace industry due to their excellent castability and high strength-weight ratios. Al–Si series alloys are typically widely employed in numerous applications for automobile components such as the alloy wheel, the supporting brackets and housings through various casting processes. Under this circumstance, the use of Al–Si alloy castings in the automotive industry has increased dramatically over the past three decades.

Nevertheless, the casting defects that are inevitably formed in conventional casting processes such as low-pressure and high-pressure die-casting play significant roles in deteriorating the mechanical properties of a cast, and many experimental and theoretical studies have been conducted to determine the effects of internal discontinuities on the mechanical properties of Al–Si alloys [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19].

To determine quantitatively the effects of micro-voids on tensile properties, many studies in this field of research have reported that the tensile properties of Al–Si alloys depend on the fractographic porosity based on the projected area of micro-voids on the fractured surface [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. Among these studies, Gokhale and colleagues suggested that the defect susceptibility of the tensile elongation to microporosity variation can be empirically described as a power law relationship, in terms of the empirical constants such as the defect susceptibility and maximum value in a defect-free condition, as in the following equation [10], [11], [12], [13], [14], [15], [16]:

$$e=e_o{(1-f)}^a$$

where e is the tensile elongation of a material with a microporosity f, e_o is the tensile elongation of a defect-free material, and a can be defined as the defect susceptibility of the tensile elongation to microporosity variation. This empirical relationship between tensile elongation and microporosity variation was also confirmed in our previous studies [16]. Similarly, the dependence of ultimate tensile strength (UTS) on microporosity variation was reported to exhibit a power law relationship according to the following equation [17]:

$$S=S_o{(1-f)}^b$$

where S and S_o are UTS of a material with a microporosity f and of a defect-free material in the engineering stress-term, respectively, and b is the defect susceptibility of the UTS to microporosity variation. However, despite the many studies in this field of research, the physical meaning of defect susceptibility in the empirical relationships in Eqs. (1), (2) has not yet been clearly described in terms of the theoretical validity of tensile deformation behaviour.

On the other hand, the constitutive model proposed in the theoretical study by Ghosh could describe the tensile deformation behaviour of a material with micro-voids in terms of the strain-related factors such as the strain-hardening exponent and strain rate sensitivity, and microporosity variation [18]. This approach means that the defect susceptibility of tensile properties to microporosity variation is practically affected by not only the microporosity but also the strain-related factors [18], [19], [20]. Therefore, the defect susceptibility can characterise the remarkable transition of deformation behaviour through the practical change of strain-related factors induced by the casting process and heat treatment of a material with a similar level of microporosity, and it has a significance to quantify the soundness of a cast, in terms of the dependence of the tensile properties on microporosity variation.

However, the original Ghosh׳s model can consider only the nominal value of microporosity but not the distribution aspect of micro-voids such as the size and the interspacing. Recently, the modified constitutive model which takes into account the geometric array of the micro-void and the microstructural factors such as the eutectic Si particles and SDAS was proposed in our previous study [21]. Thus, the theoretical model can be practically used to propose the optimal conditions of microstructural and strain-related factors minimising the adverse effects of micro-voids on tensile properties through the quantitative description of the contributions of microstructural and strain-related factors to defect susceptibility.

Therefore, the aims of the present study are to investigate the defect susceptibility of tensile properties to microporosity variation in T4-treated A356 alloy, and to understand the theoretical meaning of the empirical relation describing the defect susceptibility. In addition, it aims to verify the scientific validity of modified constitutive model through the theoretical prediction of defect susceptibility, comparing with original Ghosh׳s constitutive model [18], [19], [20], [22].