A general model for the temperature-dependent deformation and tensile failure of photo-cured polymers

Abstract

The nonlinear finite deformations and ultimate failure modes of photo-cured polymers are closely related to the ambient temperatures, typically exhibiting enhanced stretchability and a peak of ultimate break strain near the glass transition temperature ${\mathit{T}}_g$. The origin of this type of temperature-dependent failure phenomenon lies in the evolution of visco-elasto-plastic flowing dynamics as well as the alteration of polymer chain mobility during glass transition. In the past few decades, theoretical models for the strength of polymers were developed independent of the visco-elasto-plastic deformation history and the glass transition dynamics. These models could not provide reasonable explanations for the peak of ultimate break strain in photo-cured polymers, nor predict the poor stretchability at ultra-low and ultra-high temperatures. In this paper, we propose a general model for the temperature-dependent deformation and tensile failure of photo-cured polymers, in which the breaking phenomenon is dominated by a competition between the brittle failure at low temperature, the visco-plastic failure at moderate temperature and the hyperelastic failure at high temperature. Through the comparison between theoretical predictions and typical experiments, the model is proved to be efficient in predicting the deformation and failure of both photo-cured thermosets and thermoplastics.

Introduction

Photo-cured polymer is one of the most widely used material systems in adhesives, coatings, biomedical devices, shape-memory structures and polymer additive manufacturing [1], [2]. It has been long recognized that, when tested under varied temperatures, the deformation processes and ultimate failure modes of photo-cured polymers could be totally different. The polymer network behaves stiff and brittle at low-temperature glassy state, while soft and ductile at high-temperature rubbery state. For moderate temperatures near the glass transition temperature ${\mathit{T}}_g$, the network could be more ductile and the ultimate break strain might even exceed the break strain at rubbery state [3], [4]. The reason for the peak of ultimate break strain near the glass transition temperature might be the irregular network structure with fewer long chains, which is typical in photopolymerized polymers [5]. To reveal the dependency of break strain and break stress on temperatures and strain rate, Smith and co-workers finished extensive experiments on elastomers and some amorphous polymers. They found the influence of loading temperatures and strain rates were actually equivalent by using the concept of “failure envelope” [6], [7]. Gall and co-workers implemented tensile experiments for a wide range of photo-cured acrylate polymers, where the peak of break strain near ${\mathit{T}}_g$ was found to be a common phenomenon in photo-cured thermosets and some thermoplastics [8], [9], [10].

In the high-temperature rubbery state, the photo-cured polymers deform elastically until breaking [11]. The hyperelasticity of rubbery network comes from the change in its conformational entropy [12], and the network breaks when the elastic energy reaches a critical value [13]. In the low-temperature glassy state and the glass transition range, the polymers undergoes initial elastic deformation, yielding, softening, viscous flowing, hardening, and finally breaks [4]. With the help of molecular dynamic simulations, Hoy et al. revealed that the underlying deformation mechanism in glassy state is totally different from that in rubbery state [14], [15], [16]. As a result of restricted chain mobility, the conformational entropy of network remains unchanged, even under large deformation during visco-plastic flowing and hardening. The external mechanical work applied are transferred to the elastic deformation of the stiff background, and at the same time dissipated by the nonaffine stretching, rotation and vibration of individual bonds [15]. The network breaks when the nonaffine deformations of these individual bonds exceed their intrinsic strength [17], [18]. These fundamental mechanisms indicate the necessity to track the visco-elasto-plastic deformation history when predicting the ultimate failure of photo-cured polymers, especially in the glassy state and the glass transition range.

Early theoretical treatments on the temperature-dependent tensile failure in polymers were commonly decoupled from details of the visco-elasto-plastic deformation. For example Beuche et al. developed a series of molecular-level theories to describe the variation of break strength and break stress in thermoplastics, which consider the influences of temperatures and strain rates [19], [20]. But there was no unified theoretical explanation on the distinct failure modes in glassy state and rubbery state, and the complete deformation process could not be predicted. Another class of theories correlate the breaking dynamics of microscopic covalent bonds with macroscopic deformations, and the network gradually breaks with the decrease of covalent bond density [21], [22]. This type of model is proved to be successful for predicting the damage and failure of polymers with physical crosslinks [23] or dynamic bonds [24], [25]. However, the limitations of this approach include the inconvenience to identify accurate parameters for the microscopic bond breaking dynamics, as well as the difficulty to predict the brittle failure in glassy polymers.

In this paper, we propose a general finite deformation model in which the temperature-dependent failure of photo-cured polymers is dependent on the visco-elasto-plastic deformation process, and the ultimate breaking is controlled by the competition between different failure mechanisms. The model shares a similar form with conventional finite deformation visco-elasto-plastic models, while the tensile failure of polymers can be captured at the same time. Details for the composition and derivation of the proposed model are explained in Section 2. In Section 3, the model is utilized to predict some typical experiment results of photo-cured thermosets and thermoplastics.