Experimental study on z-pin bridging law by pullout test

Abstract

This paper presents an experimental study on the evaluation of bridging law for a z-pin. The relationship between the z-pin bridging force and its displacement was measured by z-pin pullout tests. The tests were carried out using three types of samples with: single small pin; 3 × 3 small-pins (three columns × three rows) and 3 × 3 big-pins. For 3 × 3 small-pins samples, a typical pullout curve with initial bonding, debonding and frictional sliding was obtained. A high peak value of the debonding force was reached before z-pin debonding started. After debonding was initiated, the pullout force dropped rapidly to a lower value, the pins were then pulled out steadily against friction. However, for samples with 3 × 3 big-pins, it was difficult to discern the peak debonding force. The major results of this study are expected to provide a better physical understanding of the mechanics and mechanisms of z-pin bridging, aside from an efficient and accurate methodology to measure the crack-bridging law.

Introduction

Through-thickness reinforcements are now widely considered as successful methods to enhance interlaminar toughness of laminated composites against delamination fracture. Since Jain and Mai [1], [2] developed the first micro-mechanics models for interlaminar mode I and mode II fractures in 1994, many research papers have been published to study the efficiency of through-thickness reinforcement and its bridging mechanisms [3], [4], [5], [6], [7]. Fig. 1 shows a double-cantilever-beam (DCB) specimen with z-pin reinforcement [8] showing mode I delamination. During delamination growth, a reinforcing z-pin provides a closure force against the opening crack. Simultaneously, the z-pin experiences elastic deformation, interface debonding from the laminates and, finally, frictional pullout. In the whole process, the functional relationship between the delamination crack-opening displacement and the closure force from a single pin is called the bridging law. The results obtained in all previous work show that the efficiency of through-thickness reinforcement is strongly dependent on the corresponding bridging law. However, a z-pin pullout is a complicated process, which is affected by many variables, for example, material properties, geometry, and interfacial parameters between the pin and the laminates. To simulate the bridging effect due to the z-pins on composite delamination, certain assumptions for the bridging law are used in all the previous numerical and theoretical studies. In Jain and Mai’s models [1], [2], the interface between stitches (or z-pins) and laminates was assumed fully frictional. The bridging force due to stitching was calculated by assuming a constant frictional shear stress between the stitch and the laminates. Later, Cox [3] presented a model of mode II delamination with a through-thickness fibre tow. Here, the bridging tow was assumed to deform in shear as a rigid-perfectly plastic material. The axial sliding of the tow relative to the laminates was frictional in nature and represented by uniform shear traction. In his numerical example, both the shear and closure tractions of the tow were given by assumed values based on observations from experiments. More recently, Liu and Mai [4] presented a theoretical model of mode I delamination of DCB with z-pinning. The bridging stress of the z-pin was calculated by a single-fibre pullout model [5], which included the whole process of z-pin pullout: elastic deformation before z-pin debonding, elastic deformation and frictional sliding during debond growth and, finally, frictional sliding. Computer simulations were given for mode I delamination fracture with z-pin reinforcement. Effects of areal density, diameter, Young’s modulus of z-pin and, especially, interfacial friction between the z-pin and laminates were studied in depth. Another study conducted by Liu et al. [6] was focused on the effect of the bridging law on z-pinned mode I delamination. Here, the bridging law was simplified to either a bi-linear or tri-linear function. These functions were determined by three parameters: maximum debonding force, maximum frictional force and displacement corresponding to debonding force. Parametric studies have been presented in order to identify the dominant factors in z-pin reinforcement. Yan et al. [7] further studied the effect of z-pinning on delamination toughness of composite laminates by using the finite element method (FEM). Different to the analytic studies, which were based on elementary beam theory, shear deformation, material orthotropy and geometric non-linearity were considered in the FEM model. The z-pin bridging law was described by a bi-linear function, which included elastic deformation and frictional sliding during z-pin pullout. The z-pin pulling-out process was simulated by the deformation of a set of non-linear springs.

From the above discussions, it is clear that there has been much effort by researchers to try to model and quantify the effects of z-pinning on delamination growth. However, the accuracies of their results and conclusions are very much dependent on the bridging law assumed based on the pullout mechanics of a single fibre, stitch or pin with varying degree of sophistication or complexity. Certainly, the most reliable bridging law is that determined by accurate pullout experiments. So far, there are no reported experimental details of the measured bridging law to justify the analytic models used in previous studies. This is seen as a major deficiency of current research on z-pinning and this paper aims to address this issue.

An experimental study on z-pin bridging was performed to determine directly the relationship between the bridging force and pullout displacement by the z-pin pullout test, which is shown in Fig. 2. Results were obtained for pullout of 3 × 3 small-pins, 3 × 3 big-pins and a single small-pin. We expect to obtain an in-depth physical understanding of the z-pin bridging mechanics and mechanisms. The experimental bridging law obtained can be used for future theoretical and numerical studies on through-thickness reinforcement due to z-pinning.