Experimental and 3D FE evaluation of crack initiation energy J 1C in Al6061-TiC composites

1. Introduction

It has been revealed that incorporating ceramic particles into Al matrix can significantly vitiate the ductility and also J _1C of the composite materials. The characteristics of particles play an important role in governing the toughness of the composites, and the deprivation of toughness is reflected to be due to cracking of particles, non-uniform distribution of particles and changes in matrix flow behavior [1–3]. It was universally perceived that an increase in volume fraction of ceramic particles (such as SiC, TiC) would decline fracture toughness of the composite, which is consistent with some published findings [4–6]. In contrast, an increase in SiC particle size would upsurge the fracture toughness, which has been confirmed by Kamat’s research [7] and Davidson’s results [2]. In their work, they studied SiC particles with a size larger than 2 μm. However, in what way the particles of fine size (≤2 μm) affect the J _1C fracture toughness of the composite has not been studied experimentally. Furthermore, previous research focussed on the properties of the composites in under aged (UA), T6 or normal temperature over aged (OA) conditions [2–4] and high temperature OA condition [8]. Nonetheless, as cast state is certainly encountered in practical applications, which has not been investigated yet, as per our knowledge. This work presents the results of a comparative study of the J _1C fracture toughness of fine TiC particle reinforced Al6061 alloy matrix composites of variable particle weight fraction (3 wt%, 5 wt% and 7 wt%) in as cast condition in comparison with available data of similar composites in the literature.

2. Material and experimental procedure

The compact tension specimens were machined by CNC wire EDM from the rectangular blocks of various proportions of TiC (3 wt%, 5 wt% and 7 wt %) reinforced Al6061 metal matrix composites as per ASTM Standard E399-83 [9]. The CT specimens having thickness to width ratio (B∕W) = 0.5 were machined so as to obtain different notch sizes of a∕W = 0.3–0.6 ratios by an increment of 0.1 as shown in our previous work [10]. The fatigue pre-cracking of the CT specimens was done in a BiSS (Bangalore Integrated Systems Solutions) servo-hydraulic testing machine with tensile cyclic loading. All fracture toughness tests were conducted using BiSS servo-hydraulic testing machine at room temperature as described in the work [11]. Load vs. CMOD data are recorded.

3. Material properties, mesh, boundary condition and extraction of J _1C used in ABAQUS for 3D finite element CT specimen

The Al6061-TiC composites of various proportions of TiC (3 wt%, 5 wt% and 7 wt %) have been considered for the elastic-plastic FE analyses. The mechanical properties of the Al6061-TiC composites material are discussed in our earlier report [12]. This Al6061-TiC composite behaves as a multilinear kinematic hardening type during plastic deformation. Consequently, for elastic-plastic finite analyses a multilinear kinematic hardening type plastic deformation was considered. In elastic-plastic FEA the plastic deformation was modeled by considering almost twenty divisions in between yield stress point and fracture point in the true stress-true strain curve of Al6061-TiC composites. In this elastic-plastic analyses a linear with a particular tangent modulus was assumed between two successive points during the plastic deformation.

The CT specimen geometry and its loading are discussed in detail [11]. During elastic-plastic fracture analyses the discretization were done without using singularity elements around the crack-tip/front. Singular finite elements during elastic-plastic fracture analyses, Courtin et al. [13] in their work clearly mentioned the utilization of singular finite elements ahead at the crack-tip/front is not essential. For 3D elastic-plastic analyses the number of elements along the z-direction (thickness) of the specimen is similar to the elastic analyses as discussed [10]. The change of J _1C along the z-direction will be same for 8–11 layers. So, 9 layers which give 8 numbers of elements were considered along the thickness of the specimen for elastic-plastic finite analyses. The magnitude of J _1C has been extracted in postprocessor (interaction) step in ABAQUS [14] software. The computed 3D FEA J _1C in ABAQUS is similar manner to the earlier report [13]. Domain integral method coding was made in ABAQUS software tool to determine the J _1C . So, one can define the nodes at crack-front for 3D and also specify the number of contours to extract J _1C values. ABAQUS provides a procedure for numerical evaluation of the J, based on the virtual crack extension/domain integral methods [15,16]. The method of extraction of J _1C adopted in ABAQUS is user friendlier and provides better results for coarse meshes [14].

4. Results

A characteristic load vs. CMOD curve for the various composites with variable crack lengths is shown in Fig. 1 (Al6061 + 3 wt%TiC), Fig. 2 (Al6061 + 5 wt%TiC) and Fig. 3 (Al6061 + 7 wt%TiC). The crack propagation energy (E _P ) evaluated from Figs 1–3 and the total absorbed energy (E _T ) = E _M + E _P were computed. The calculated results of J _1C , E _P and E _T determined from load vs. CMOD curves are given in Table 1. The fracture initiation energy (J _1C ), plastic energy consumed until fracture (E _P ) and the total energy (E _T ) typically for a∕W = B∕W = 0.5 of all Al6061 + TiC composites are illustrated in Fig. 4.

Next, 3D FE nonlinear analyses of CT fracture specimen for various crack lengths (a∕W = 0.3–0.6) of all Al6061-TiC composites were carried out to extract the J _1C values. During finite element analysis we considered five contours ahead at the crack-front. While extracting J _1C , the first contour is very near to the crack-front and will be neglected, remaining average values of four contours were considered. The method of extraction of J _1C was similar to Kodancha and Kudari’s work [17]. Initially, the extracted J _1C from ABAQUS [14] post processor for various crack lengths were plotted against the thickness along the crack-front in z-direction for critical load. Figures 5–7 show the variation of crack initiation toughness J _1C vs. thickness along crack-front of the specimen in z-direction for a∕W = 0.3–0.6 with B∕W = 0.5 of all Al6061-TiC composites under critical load.

5. Discussion

The apparent crack initiation toughness J _1C , was assessed rendering to Rice’s equation: J 1 C = 2 E M / B ( W − a )(1) where E _M is the energy expended until the maximum load, B the specimen thickness, W the specimen width, and a the initial crack length. The particular value of a was measured using a low magnification microscope after the fracture of the specimen according to ASTM standard E399-83 [9].

It can be clearly noted that the apparent crack initiation toughness and total absorbed energy increases for 5 wt%TiC composite and then decreases for 7 wt%TiC composite with respect to 3 wt%TiC composite.

As we can see in Figs 5–7 the value of J _1C is more at the middle compare to the edge of the CT fracture specimen. This indicates that the stress filed ahead at the crack-front is more at the middle compare to the edge of the CT fracture specimen. As in case of elastic-plastic or ductile materials the higher stress field will rises the plastic core (plastic zone) region ahead at the crack-front. This enlargement of plastic zone ahead at the crack-front will initiates fracture early. Also, the 3D FEA results were compared with the experimental results of various a∕W ratios for different Al6061-TiC composites as depicted in Fig. 8. It is observed from Fig. 8 that the extracted FE results of J _1C at the center of specimens are in good agreement (within in ±3% discrepancy) with experimental results rather than the surface J _1C FE results. For 3D fracture finite element simulations it is important to take the estimated J _1C results at the center rather on the surface of the CT specimen. Also from Fig. 8 we can observe that there is decreasing trend of J _1C fracture toughness with increasing a∕W ratios of the specimen for composites.

The influence of particle size and volume fraction of the composite on its fracture toughness is predicted by a model proposed by Rice and Johnson [18] which is later modified by Hahn and Rosenfield [19]. An expression established by Hahn and Rosenfield is given by Eq. (2): J 1 C / 2 σ y ( 1 − v 2 ) = λ .(2) For the variable 3 wt% (1.7 vol.%), 5 wt% (2.9 vol.%) and 7 wt% (4.0 vol.%) of TiC particle composites in the present investigation, values are calculated to be 11.1 μm, 8.5 μm and 7.2 μm respectively. Input the measured data J _1C into J _1C ∕2𝜎 _y (1 − v ²), J _1C ∕2𝜎 _y (1 − v ²) are then plotted in Fig. 9 as a function of 𝜆 as compared with available results for 25 vol% 9.5 μm SiC_P/Al6061 [6] and Davidson’s data [2]. Clearly, the experimental data for both 9.5 μm SiC particle (15% and 25%)/Al6061 and 6.6 μm SiC_P (15%)/Al 2024 lie on or close to the line drawn using Eq. (2), hence confirming to the Hahn and Rosenfield’s [19] expression.

In the present work with 2 μm TiC reinforced composites, the critical strain exceeds the inter-particle space which results in invalidity of Hahn and Rosenfield’s model. Also from Fig. 9 we can propose that by increasing the size of TiC to 5–6 μm and with higher proportions of the reinforcement, Hahn and Rosenfield’s formulation will be satisfied. As a result the expected region for higher volume fraction (10–15%) and size (5–10 μm) of TiC reinforced Al composites to satisfy Hahn and Rosenfield’s equation would be somewhere near the circle marked on the line of J _1C ∕2𝜎 _y (1 − v ²) = 𝜆. This prediction is validated by the research findings of Rabiei et al. [20] which showed that Hahn and Rosenfield assumption is almost valid only in the range of 5–10 μm reinforcements.

The apparent crack initiation toughness and total absorbed energy increases for 5 wt%TiC composite and then decreases for 7 wt%TiC composite with respect to 3 wt%TiC composite. It is observed that the extracted FE results of J _1C at the center of specimens are in good agreement (within in ±3% discrepancy) with experimental results rather than the surface J _1C FE results. The fracture toughness decreases with increasing crack length of the specimen because of decrease in load carrying capacity of the specimens. Al6061-TiC composites exhibit higher fracture toughness values than their counterparts Al6061-SiC composites even with lower volume fractions of TiC reinforcements.

Conflict of interest

None to report.