مدل شکست خستگی برای سیستم های سازگار پلیمری Fatigue Failure Model for Polymeric Compliant Systems

Fatigue is one of the major failure mechanisms in engineering structures [1]. Time-varying cyclic loads result in failure of components at stress values below the yield or ultimate strength of the material. Fatigue failure of components takes place by the initiation and propagation of a crack until it becomes unstable and then propagates to sudden failure. The total fatigue life is the sum of crack initiation life and crack propagation life. Fatigue life prediction has become important because of the complex nature of fatigue as it is influenced by several factors, statistical nature of fatigue phenomena and time-consuming fatigue tests. Though a lot of fatigue models have been developed and used to solve fatigue problems, the range of validity of these models is not well defined. No method would predict the fatigue life with the damage value by separating crack initiation and propagation phases. The methods used to predict crack initiation life are mainly empirical [2] and they fail to define the damage caused to the material. Stress- or strainbased approaches followed do not specify the damage caused to the material, as they are mainly curve fitting methods. The limitation of this approach motivated the development of micromechanics models termed as local approaches based on continuum damage mechanics (CDM). The local approaches are based on application of micromechanics models of fracture in which stress/strain and damage at the crack tip are related to the critical conditions required for fracture. These models are calibrated through material specific parameters. Once these parameters are derived for particular material, they can be assumed to be independent of geometry and loading mode and may be used to the assessment of a component fabricated from the same material. For some compliant structures, the desired motion may occur infrequently, and the static theories may be enough for the analysis [3]. However, by the definition of compliant mechanisms, deflection of flexible members is required for the motion. Usually, it is desired that the mechanism be capable of undergoing the motion many times, and design requirements may be many millions of cycle of infinite life. This repeated loading cause fluctuating stresses in the members and can result in fatigue failure. Failure can occur at stresses that are significantly lower than those that cause static failure [3]. A small crack is enough to initiate the fatigue failure. The crack progresses rapidly since the stress concentration effect becomes greater around it. If the stressed area decreases in size, the stress increases in magnitude, and if the remaining area is small, the member can fail. A member failed because of fatigue showing two distinct regions. The first one is due to the progressive development of the crack, while the other one is due to the sudden fracture. Premature or unexpected failure of a device can result in an unsafe design.The consumer confidence may be reduced in products that fail prematurely. For these and other reasons, it is critical that the fatigue life of compliant mechanism be analyzed. Although fatigue failure is difficult to predict accurately, an understanding of fatigue failure prediction and prevention is very helpful in the design of compliant mechanisms. The theory can be used to design devices that will withstand these fluctuating stresses. Several models are available for fatigue failure prediction. The stress-life and strain-life models are commonly used in the design of mechanical components [3]. These theories are appropriate for parts that undergo consistent and predictable fluctuating stresses. Many machine components fit into this category because their motion and loads are defined by kinematics of the mechanism. There are three stress cycles with which loads may be applied to the component under consideration. The simplest being the reversed stress cycle (Figure 1(a)). This is merely a sine wave where the maximum stress and minimum stress differ by a negative sign. An example of this type of stress cycle would be in an axle, in which every half turn or half period as in the case of the sine wave, the stress on a point would be reversed. The most common type of cycle found in engineering applications is where the maximum stress and minimum stress are asymmetric (the curve is a sine wave), not equal, and opposite (Figure 1(b)). This type of stress cycle is called repeated stress cycle. A final type of cycle mode is where stress and frequency vary randomly (Figure 1(c)). An example of this would be hull shocks, where the frequency magnitude of the waves will produce varying minimum and maximum stresses. Predicting the life of parts stressed above the endurance limit is at best a rough procedure. For the large percentage of mechanical and structural compliant systems subjected to randomly varying stress cycle intensity (e.g., compliant automotive suspension and compliant aircraft structural components, etc.), the prediction of fatigue life is further complicated. The normal stress-life and strain-life models cannot be adopted in the fatigue prediction. Models such as continuum damage mechanics (CDM) can be used in dealing with this situation. Polymers are predominantly used in the design of compliant mechanisms [3]. It is important to use the nonlinear characteristics of polymers to analyse the performance of compliant systems. Thermoplastic polymers like polypropylene exhibit a viscoelastic material response [4]. It has been frequently noted that with certain constitutive laws, such as those of viscoelasticity and associative plasticity, the material behaves in a nearly incompressible manner [5]. The typical volumetric behavior of hyperelastic materials can be grouped into two classes. Materials such as polymers typically have small volumetric changes during deformation and those that are incompressible or nearly-incompressible materials [6]. An example of the second class of materials is foams, which can experience large volumetric changes during deformation, and these are compressible materials. This implies that most polymers are nearly incompressible. In general, the response of a typical polymer is strongly dependent on temperature [7]. At low temperatures, polymers deform elastically like glass; at high temperatures, the behaviour is viscous like liquids; at moderate temperatures, the behaviour is like a rubbery solid. Hyperelastic constitutive laws are intended to approximate this rubbery behaviour. Polymers are capable of large deformations and subject to tensile and compression stress-strain curves [8]. The simplest yet relatively precise description for this type of material is isotropic hyperelasticity [8]. The fatigue failure of thermoplastics polymers generally develops in two phases [9]. First, the material accumulates fatigue damage (i.e., in the initiation phase), which ultimately leads to the formation of visible crazes. The crazes further grow, form cracks and propagate (i.e., in the propagation phase) until the final failure occurs. In general, the damage process in polymers is regarded as the formation and development of microdefects and crazes within an initially perfect material. The material remains the same but its macroscopic properties change with its microscopic geometry [10]. In polymers, craze formation is generally believed to be one of the main causes of material damage, which is both a localized yielding process and the first stage of fracture. Crazes are usually initiated either at surface flaws and scratches or at internal voids and inclusions and affect significantly the subsequent deformation and bulk mechanical behaviors of polymers [11]. The continuum damage mechanics (CDM) first introduced by Kachanov and developed within the framework of thermodynamics discusses systematically the effects of microdefects on the subsequent development of microdefects and the states of stress and strain in materials. It has been applied to fatigue and fracture of different materials. In this paper, an isotropic damage evolution equation for finite viscoelasticity characteristic of polymeric CMs is proposed, which is based on the CDM. A new damage model is developed to establish the fatigue life formula for such compliant systems. The compliant material is idealized as an isotropic hyperelastic material. A commonly used polymeric material, low density polypropylene (LDP) was tested to obtain the fatigue life as a function of the strain amplitude.