Micromechanical model for competition between intergranular and intragranular fracture in 7××× aluminum alloys

ZHANG Xin-ming(张新明), LIU Wen-hui(刘文辉), TANG Jian-guo(唐建国), LIU Sheng-dan(刘胜胆)

School of Materials Science and Engineering, Central South University, Changsha 410083, China

Received 28 July 2006; accepted 15 September 2006

Abstract: The 7××× aluminum alloys having a microstructure with precipitate free zones (PFZ) nearby the grain boundary, have received a great deal of attention due to their high strength, light mass, and yet poor fracture toughness. Experimental investigation into the effect of microstructure on the ductility was well established and comprehensive in the literature. A micromechanical model using a unit cell including some voids and relevant microstructural features was created. The competition between intergranular and intragranular fracture was investigated by comparing the void growth velocity between PFZ and matrix. The effects of void aspect ratio, relative PFZ volume, orientation of PFZ on the ductility of 7××× aluminum alloys were analyzed. The results show that the model can explain the effect of microstructure on the competition between intergranular and intragranular fracture.

Key words: aluminum alloys; micromechanical model; unit cell; intergranular fracture; intragranular fracture

1 Introduction

The 7××× aluminum alloys that are widely used for structural application usually possess high strength level but relatively poor toughness. It will be useful to know how the microstructure of alloys affects the fracture behavior, then design an appropriate heat treatment to get better toughness without many strength loss. Many experimental researches have been done to investigate the effect of microstructure on fracture toughness. But few mechanical models have been founded to analyze the effect of microstructure on the fracture toughness because of the complexity of microstructure of 7××× aluminum alloys. LIU et al [1-2] established a model for high strength aluminum alloys to present a nonlinear relation between the fracture toughness, tensile ductility of the alloys and the characteristics of constituents, dispersoids, and precipitates within the alloys. PARDOEN et al[3] investigated the competition between intergranular and intragranular fracture by using a bilayer damage model, and the void growth and coalescence were modeled using an enhanced Gurson-type model, but the bilayer model can not explain the effect of PFZ orientation and fracture path. In this paper a micromechanical model for 7××× aluminum alloys consisting of PFZ and matrix is created to analyze the effect of microstructure on the ductility. The effects of void aspect ratio, relative volume of PFZ, and orientation of PFZ on the ductility of 7××× aluminum alloys are analyzed by comparing the void growth velocities between PFZ and matrix, and finally the fracture path is discussed.

2 Finite element method

It is suggested that fracture proceeds by the nucleation of voids and subsequent coalescence of these voids. Here the size and spacing of intergranular precipitates are assumed to control the initial size and spacing of grain boundary nucleated cavities, and the size and spacing of intragranular dispersoids are assumed to control the initial size and spacing of intragranular nucleated cavities.

The plain strain model is shown to capture the mechanism of deformation of materials observed and reported in the literature. AL-ABBASI and NEMES[4] modeled the effective properties of dual phase steels by using the plain strain model. PARDOEN and HUTCHINSON[5] used a plain strain model to predict the trends in toughness of ductile metals. In this paper, a plain strain model was used to analyze the mechanical properties of 7××× alloys.

Because the grain boundary shearing is suppressed at the triple point due to the plastic constraint of neighboring grains, and the deformation of the PFZ parallel to Y direction is small, it is assumed that voids do not exist at the triple point and PFZ parallel to Y direction for simplicity. The idealized microstructure is shown in Fig.1, and the parameters to be introduced in the micromechanical model are shown in Table 1, where the subscripts p and g denote PFZ and grain interior.

Fig.1 Idealized microstructure and corresponding unit cell

Table 1 Mechanical parameters definition

In the present work, a constant Y direction increment of displacement is prescribed while the X direction increment is adjusted using an iterative method until the desired stress triaxiality T is attained. In this paper, it isn’t intended to give quantitative prediction of the ductility. The reasonable values of mechanical parameters of the uniaxial elastic and plastic tensile properties for the material in the grain interior and the PFZ for typical 7000 aluminum alloys have been given by PARDOEN and DUMONT [3].

The constitutive equation is shown in Eqn.(1), and the following set of parameters have been chosen for analyzing the mechanical characters of 7××× alloys: E_p=E_g=E=70 GPa, ν_p=ν_g=0.33, n_p=0.3-0.35, n_g=0.05.

            (1)

3 Results and discussion

PARDOEN assumed that the point where the effective stress drops rapidly is the onset of void coalescence due to localization [6-7]. In this paper, the void volume fraction of PFZ and matrix before coalescence is compared. Various physical parameters of material properties, such as the loading condition and the microstructure will influence the void growth and coalescence within PFZ and matrix. Here, the parameters that can be experimentally varied by heat treatments are considered. Of course, aluminum alloys never show completely intergranular fracture or intragranular fracture. The parameter choices used in the computations in this work are not intended to give quantitative prediction of the ductility and of the exact locus of failure model transition, but to demonstrate how they affect the void volume fraction of PFZ and matrix. The following set of parameters have been chosen with stress triaxiality T remaining unchanged: s_0g/s_0p=6, f_pv=f_gv= 0.01, m_g=3, m_p=6, R=0.1, T=0.5, W_g=W_p=3, L_y/L_x=4, a=60?, only one parameter of them has changed to investigate how it affects the void volume fraction within PFZ and matrix.

It is well known that slow quenching rate will induce wide PFZ, and the precipitate will be coarser, which is harmful to toughness. However, PFZ reduces the stress concentration at grain boundaries for lower yield stress than the matrix, which will be beneficial to toughness. Here f_pv is assumed to remain constant. The wider the PFZ, the larger the void volume in PFZ will be.

Fig.2 shows the effect of relative PFZ volume on the evolution of void volume fraction of PFZ and matrix with the strain of Y direction E_y. The calculation results show that the precipitate size plays a key roll. For R=0.15, the voids of PFZ grow rapidly, and the alloys fail at small strain by intergranular fracture; for R=0.05, the precipitate in PFZ is small, which offers an opportunity for the void growth within matrix without too many void growth within the PFZ, and alloy may fail at large strain by intragranular fracture. This agrees with the facts observed in experiments[8].

Fig.2 Effect of relative PFZ volume on void volume fraction of PFZ and matrix

For the same condition of different 7000 series alloys, the value of s_0g/s_0p can indicate the contents of solute alloy based on the assumption that the PFZ strength is comparable to that of the alloy as solution treated [9]. For high solute alloy, the value of s_0g/s_0p is large. For the same 7000 series alloy in different aging state, the value of s_0g/s_0p can indicate the different aging time. The under aging specimen has small value of s_0g/s_0p (=4). With the aging time increasing, the value of s_0g/s_0p increases. In the peak aging state, the value of s_0g/s_0p will be maximal (=8), and the localization of deformation is strongest for the peak aging alloys because of the strength difference between the matrix and the PFZ at the grain boundary, which creates strain localization that may induce grain boundary failure. In the over aging state, with the aging time increasing, the value of s_0g/s_0p decreases (=6).

Fig.3 shows the effect of s_0g/s_0p on the void volume fraction of PFZ and matrix. For the case of s_0g/s_0p=4, voids in matrix coalesce before that within PFZ, and alloy is more likely to fail by intragranular fracture; for s_0g/s_0p=8, voids coalesce within PFZ, and alloy is more likely to fail by intergranular fracture; for s_0g/s_0p=6, the failure model will be the mixture of intragranular fracture and intergranular fracture. This agrees with the experimental results of DUMONT et al [10]. The increase of grain stress is accompanied with an increase of proportion of grain boundary (GB) failure and much lower fracture toughness.

Fig.3　Effect of s_0g/s_0p on void volume fraction of PFZ and matrix

Fig.4 shows the effect of initial PFZ void aspect ratio on the void volume fraction of PFZ and matrix during deformation. For the case of W_p=6, PFZ voids start to coalesce within PFZ at small strain; for W_p=1, voids in matrix coalesce before that within PFZ, and alloy is more likely to fail by intragranular fracture.

Fig.4　Effect of PFZ void aspect ratio on void volume fraction of PFZ and matrix

The fracture path initiates and follows a plane of maximum shear stress, so the GB fracture preferentially occurs on the GBs inclining about 45?to the tensile axis. TAKESHI et al[11] showed grain boundary oriented 45? to the external load provided a more favorable path for crack. But the calculation results do not show that voids within PFZ oriented 45° to the external load grow more rapidly than the others. Fig.5 shows the effect of PFZ direction on the void volume fraction of PFZ and matrix. With the grain boundary angle a oriented to the external load (Y) increasing, the void growth within PFZ and matrix becomes more rapid. For the case of grain boundary angle of 30?, because the change of strain in PFZ is small, the void growth velocity is very small, and alloys seem to preferentially fail by intragranular fracture.

According to the simulation results, the growth of voids within PFZ and matrix can be sorted into two stages. At small deformation, the void growth in PFZ is dominant. Because of low yield stress s_p, voids tend to grow within PFZ firstly, and the void volume fraction grows more quickly than that of matrix; then the growth velocity of PFZ drops due to the matrix stress reaching yield stress and the high work hardening rate n_p. If voids coalesce within PFZ, alloy will fail by intergranular fracture. In Fig.4, the case of W_p=6 shows the condition of intergranular fracture. Due to the high yield stress s_g, the voids within matrix grow slowly at the beginning of deformation, then grow rapidly for its low work hardening rate n_g. Small change of stress in matrix will cause the strain to change quickly. If voids in matrix coalesce before that within PFZ, alloy has a trend to occur intragranular fracture. In Fig.4, the case of W_p=1 shows the condition of intragranular fracture.

Fig.5　Effect of PFZ direction on void volume fraction of PFZ and matrix

The competition between intergranular and transgranular failure can be qualitatively understood in the following way (Fig.6). Due to the different flow properties, the critical porosities for PFZ and matrix will be different, and the critical porosity for PFZ is higher than that of matrix. In Fig.6, OA represents the evolution of voids volume fraction of matrix, and OC represents the voids volume fraction of PFZ. If voids in matrix coalesce before that within PFZ (OA-OC₁), alloys have a trend to fail by predominantly intragranular fracture. OA-OC₂ represents the case of intergranular fracture. From the calculation results, if the matrix parameters remain unchanged, there is small change with the matrix’s void volume fraction (OA), and the change of PFZ parameters will change the position of C. The increase of R and W_p will cause the point C to move toward the left hand. The longer the distance of SC₂, the easier the alloys fail by intergranular fracture, or much more fraction of intergranular fracture occurs. The increase of s_0g/s_0p will cause the point A to move toward the right hand.

Fig.6 Competition between intergranular and transgranular fracture

Fig.7 shows the contours of equivalent stress with Y directional strains of 5% and 10%. All show the heterogeneous distribution of stress. In matrix, it can be found that along the path oriented 45? to the Y direction, the equivalent stress is larger than that at other places.

Fig.7 Contours of equivalent stress

When alloys fail by transgranular fracture, for the case of s_0g/s_0p=4, the equivalent stress along the path oriented 45? to the Y direction is larger than that at other places according to the calculated results. If particles are uniformly distributed in matrix, voids tend to nucleate, grow and coalescence along the path where the deformation is larger than that at other places. The schematic of transgranular fracture is shown in Fig.8.

The optical microscopy observation of an arrested crack in 7150 is shown in Fig.9 [12]. Many regions of transgranular fracture show the ‘V’ shape fracture edge, which is quite similar to the transgranular fracture model as Fig.8.

Fig.8 Model for transgranular fracture

Fig.9 Optical section of arrested crack in 7150 alloy

4 Conclusions

A micromechanical model for 7××× aluminum alloys consisting of PFZ and matrix is created, which provides trends about the effect of the micromechanical parameters on the growth of voids within PFZ and matrix. The effects of void aspect ratio, relative PFZ volume, orientation of PFZ on the ductility of 7××× aluminum alloys are analyzed by comparing the void growth velocity between PFZ and matrix, and the fracture path is discussed. It can be applied to problems involving competition between the failure in a soft and a hard zone. This model will prove valuable for determining optimum microstructure for 7××× aluminum alloys while minimizing the amount of required experimental work. In addition, it provides a tool for understanding the mechanics and mechanisms of deformation taking place in such materials, and can be used in developing a predictive theory of deformed solids for both ductile failure and failure under fatigue loading. It provides a tool to optimize the microstructure to get superior mechanical properties.

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(Edited by YUAN Sai-qian)

Foundation item: Project(2005CB623706) supported by the National Basic Research Program of China

Corresponding author: LIU Wen-hui; Tel: +86-731-8830265; E-mail: wealth9733221@sohu.com