An evaluation of the temperature dependence of cohesive properties for two structural epoxy adhesives

Cohesive modelling provides a more detailed understanding of the fracture properties of adhesive joints than provided by linear elastic fracture mechanics. A cohesive model is characterized by a stress-deformation relation of the adhesive layer. This relation can be measured experimentally. Two parameters of the stress-deformation relation are of special importance; the area under the curve, which equals the fracture energy, and the peak stress. The influence of temperature of these parameters is analyses experimentally and evaluated statistically for two structural epoxy adhesives in the span from of -40°C to +80°C. The adhesives are used by the automotive industry and a temperature span below the glass transition temperature is considered. The results show that that temperature has a modest influence on the adhesives Mode I fracture energy. For one of the adhesives, the fracture energy is independent of the temperature in the evaluated temperature span. In mode II, the influence of temperature is larger. The peak stresses decreases almost linearly with an increasing temperature in both loading cases and for both adhesives. Introduction The automotive industries are striving to minimize the weight of their products in order to reduce the fuel consumption and thereby the emissions. In addition, the manufacturers are facing requirements to improve the crashworthiness. This is often at the expense of an increased weight. By using lightweight materials such as aluminium or composites in the body structure and combine these with tough material, e.g. steel, at impact zones, a more optimized solution can be obtained. Today, the majority of body structures consist of alloyed steel sheets that are joined by spot welds. A disadvantage with spot welds is the difficulty to join steel with aluminium alloys. This has put focus on modern crash resistant epoxy adhesives that enable joining of dissimilar materials. When using adhesives in a body structure it is in terms of crashworthiness required that the adhesive layers remain intact during a crash. This secures that bonded material deform in a predicted mode to dissipate the kinetic energy safely. With cohesive modelling, a stress-deformation relation is used to characterize the strength of an adhesive layer. This is a constitutive relation on a structural length scale between the traction exerted on the interfaces of the adhesive to the adherends and the separation of the interfaces. The separation equals the deformation of the adhesive layer. In the sequel, this relation is denoted a stress-deformation law. Fig. 1 indicates peel and shear deformation. These are characterized by peel deformation, w, and peel stress, σ; and shear deformation, v, and shear stress, τ. The success of this characterization is due to the high toughness of modern adhesives. With brittle adhesives, we can expect to have to model the details of the fields more accurately. Fig.1. Deformation modes with corresponding stress and deformation of an adhesive layer with initial thickness t. Left: Mode I, peel. Right: Mode II, shear. Fig.2. Stress-deformation relations for an adhesive layer. The strength of adhesively bonded multi-material build-up structures can be adequately predicted using cohesive modelling and the finite element method, cf. e.g. [1]. This modelling provides a more detailed understanding of the fracture properties of adhesive joints than can be achieved with fracture mechanics. Methods to measure the cohesive properties in Mode I, II and in mixed mode loading are summarized in [2]. Typical stress-deformation relations are shown in Fig. 2. Two parameters of these relations are of special importance; the area under each curve which equals the fracture energy and the peak stress. An automotive body structure is required to fulfil its requirements at all working temperatures. The relevant areas of a car body for which adhesives are of interest normally suffers the temperature range -40°C ≤ T ≤ 80°C. Some studies of the influence of temperature have been performed. In [3] it is shown that the stress-deformation relation for the epoxy adhesive DOW Betamate XW 1044-3 (DB1044) is strongly temperature dependent in Mode I. In this study, the entire stress-deformation law is evaluated at seven equally distributed temperatures with ten repeated experiments at each temperature. In [4] it is shown that the fracture energy for an structural epoxy adhesive decreases in the temperature region 0.7 < T / Tg < 1.0, where Tg denotes the glass transition temperature. For most epoxies it is about 100°C. Furthermore, it is shown that the yield strength decreases with increasing temperature and increases with increasing strain rate. In [4], the fracture energy is determined using an unstable specimen and the experiments are evaluated using linear elastic fracture mechanics (LEFM). That is, the entire cohesive relation is not captured. Cohesive models are implemented in finite element software to simulate the behaviour of adhesively joined structures. To perform these analyses considering temperature, the temperature dependence of the adhesive layer has to be taken into account. The previous studies do not provide all the necessary data and therefor a cohesive model cannot yet be established. This implies that new experiments need to be performed. An adhesive that is of current interest by the automotive industry is the crash resistant epoxy SikaPower498 (SP498). In this work, temperature studies are performed on this adhesive in Mode I and Mode II. Statistical methods are used to evaluate the influence of temperature on the two important parameters, peak stress and fracture energy. Moreover, the results in [3] are re-evaluated using statistical methods. Methods The two most frequently used test specimens to measure Mode I and Mode II fracture properties for adhesives are the double cantilever beam (DCB) and the end notched flexure specimen (ENF) cf. Figs. 3 and 4, respectively. These specimens are used in the studies in [3] and [4]. The specimens Peel w,v (μm) σ ,τ ( M P a) Shear each consist of two adherends that are partially joined by an adhesive layer. The part of the specimens that is not joined by an adhesive layer is considered as a crack, and the start of the adhesive layer is denoted the crack tip. Fig.3. Deformed DCB test specimen with out of plane width b. For the DCB specimen the adherends are separated by a prescribed deformation ∆ and the reaction force, F, is measured. The stress-deformation relation for the DCB specimen is given by Eq. 1 in which J is derived either by using beam theory, cf. [5], or by using the path independent J-integral, cf. [6].       ≡ = b F w w J w θ σ sin 2 d d d d ) ( , (1) where, θ is the rotation of the loading points and b is the specimen width. Fig.4. Deformed ENF test specimen with out of plane width b. A properly designed ENF-specimen gives almost a state of pure shear at the crack tip. A recently developed method to measure J for the ENF specimen is presented in [7] and is validated showing good agreement to input data using finite element analysis in [8]. From this method the stressdeformation relation of the adhesive layer is given as [ ]       + − − ≡ = 3 2 1 sin sin sin ) 1 ( d d d d ) ( θ η θ θ η τ b F v v J v (2) ∆ + h + t t + w