Fracture resistance curves of wood in the longitudinal direction using digital image correlation technique

Highlights

• Digital image correlation (DIC) technique is applied in three-point-bending fracture test.

• The K_R and G_R curves are constructed based on the experiment.

• Wood fracture in the longitudinal direction is studied by combining K_R curves and G_R curve.

• The fracture toughness becomes larger, but the fracture energy gets smaller with the increase of notch-to-depth ratio.

• K_R and G_R curves both have three stages with the same dividing points and different evolution shapes.

Abstract

This paper studies the fracture characteristics of wood in the longitudinal direction by combining K_R curves and G_R curve for fracture resistance ability analysis. Three-point-bending fracture test is carried out on the notched specimens. Digital image correlation (DIC) technique is applied to obtain the crack opening displacement and then calculate the equivalent crack length according to the double K fracture criterion. The K_R and G_R curves are constructed based on the experiment. The results show that the fracture toughness becomes larger but the fracture energy gets smaller with the increase of notch-to-depth ratio. Both the two curves show that the crack resistance ability is approximately improved when the notch-to-depth ratio increases. Through comparing K_R and G_R curves of the same specimen, it is seen that although these two kinds of fracture resistance curves have different evolution shapes, they both have three stages with the same dividing points, and they both can be used to analyze the quasi-brittle fracture process of wood.

Introduction

As a green and natural engineering material, wood has been vastly used in constructions. However, due to the natural defects, such as joints, wormholes, and tiny cracks, the stress concentration and crack propagation usually occur in wood when it is under external load, which would cause fracture failure. There is a fracture process zone (FPZ) in front of the crack tip during the quasi-brittle fracture process of wood [1]. Microcracks exist in this FPZ, which reduce the singular stress field by energy dissipation and stress redistribution [2], [3], [4]. As a result, the fracture resistance effect as R-curve is constructed in order to analyze the FPZ effect on quasi-brittle fracture property [5].

Cohesive zone model, which suggests a strain softening behavior in FPZ, has been proved to be very effective to analyze the quasi-brittle fracture behavior [6], [7], such as fictitious crack model [8], blunt smeared crack model [9], size effect model [10]. As for wood, considering the accuracy and simplicity of the calculating results, the bilinear softening model based on cohesive zone model was used to describe the constitutive relationship in FPZ [11], as shown in Fig. 1. Fig. 1a schematically illustrates the quasi-brittle fracture process by the load-deflection curve, which is divided into three stages: linear stage, micro-cracking stage and crack-bridging stage. The divided points correspond to the initial-cracking load P_ini and the peak load P_max respectively. The latter two stages, which are caused by the microcracks and failure crack respectively, constitute the strain softening part. Fig. 1b shows the corresponding constitutive relations [5], [12]. The horizontal axis w represents the crack opening displacement (COD), and the vertical axis represents the normal stress σ at the initial crack tip. When σ reaches its ultimate stress f_t, which corresponds to P_ini, the crack tip begins to form a cohesive zone. The simplified bilinear relation is used to illustrate the decreasing σ-w curve in the then strain softening stage. The intersecting point of the two lines represents the critical stress σ_s, corresponding to P_max. After P_max, the fracture crack begins and propagates rapidly. When σ decreasing to zero, w reaches the maximum value w_c.

The area below the σ-w curve in the softening part is usually called cohesive fracture energy G_f, which can be understood as the energy required to completely separate the fracture surface. G_f can be divided into two parts [5]: micro-fracture fracture energy G_fμ and crack-bridging fracture energy G_fb (Fig. 1b). For quasi-brittle fracture, the G_R curve (fracture energy resistance curve) is used to reflect the ability of material to resist crack propagation, and it is obtained by the relation between fracture energy release rate G and the crack propagation length Δa. It is apparent that G_R curve is related with the bilinear softening model, and the parameters of the bilinear softening relation shown in Fig. 1b can be determined by the G_R curve [12].

On the other hand, the crack propagation is also directly dependent on the stress field around the crack tip, which is the stress intensity factor K, determined by the stress and crack length at the crack tip [13], [14]. At first, K was used to describe the fracture property of brittle materials. For quasi-brittle materials, the equivalent crack a_e was introduced and applied to obtain K by linear elastic fracture mechanics. For example, the double-K fracture criterion was used to describe the quasi-brittle fracture property of heterogeneous materials like concrete [15], in which the initial cracking fracture toughness $K_I^{\text{ini}}$ and the failure fracture toughness $K_I^{\text{un}}$ were the fracture parameters to divide the fracture process according to crack initiation and development. As illustrated by Fig. 1(a), K_Iⁱⁿⁱ and K_I^un correspond to P_ini and P_max respectively. When the stress intensity factor at the crack tip K < K_Iⁱⁿⁱ, no crack appears at the crack tip; when K = K_Iⁱⁿⁱ, the crack begins to propagate; when K_Iⁱⁿⁱ < K < K_I^un, the micro-cracks develop steadily; when K = K_I^un, the crack begins its unstable stage; when K = K_I^un, the failure crack develops unsteadily. Same with G_R curve, one can build the relationship between K and Δa, named as K_R curve, which can be used to judge the fracture process.

From the above analysis, there must be some relation between G_R and K_R relations, as well as that the crack length are necessary to determine these fracture parameters. However, it is difficult to measure the crack length accurately during the fracture test using only strain gauges. Recently, digital image correlation (DIC) method, which is an optical non-contact measurement technique, has been used to analyze two-dimensional deformation of sample surfaces by comparing the image with the reference image before deformation [16]. DIC method is simple and insensitive to environmental noise. With high-quality speckle digital image and good correlation algorithm, reliable and accurate analysis results can be arrived. It has been proved that DIC can be used to obtain the FPZ evolution in the quasi-brittle fracture [17], [18], as well as reveal the nonuniform failure process and failure mechanism of concrete interface by strain development [19], [20]. Moreover, DIC has been used in wood fracture research before, to measure the COD evolution and then calculate the equivalent crack length [16].

In this study, the K_R and G_R fracture resistance curves of wood in its longitudinal direction was researched with the equivalent crack length determined by the DIC technique. The three-point-bending (3-p-b) fracture test was taken on Douglas fir (Pseudotsuga menziesii), and the fracture toughness was calculated according to the double-K fracture criterion, and then the K_R curve was built. On the other hand, the G_R curve was established according to the compliance method. At last, the difference and relation between K_R and G_R curves were discussed.