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Viscoelastic Creep Crack Growth: a Review of Fracture Mechanical Analyses

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Viscoelastic Creep Crack Growth: a Review of Fracture Mechanical Analyses Mechanics of Time-Dependent Materials 1: 241–268, 1998. 241 c 1998 Kluwer Academic Publishers. Printed in the Netherlands. Viscoelastic Creep Crack Growth: A Review of Fracture Mechanical Analyses W. BRADLEY1, W.J. CANTWELL2 and H.H. KAUSCH2 1Department of Mechanical Engineering, Texas A&M University, College Station, TX, U.S.A.; 2Materials Science Department, EPFL, DMX-LP, Swiss Federal Institute of Technology, 1015 Lausanne, Switzerland (Received 8 February 1997; accepted in revised form 2 October 1997) Abstract. The study of time dependent crack growth in polymers using a fracture mechanics approach has been reviewed. The time dependence of crack growth in polymers is seen to be the result of the viscoelastic deformation in the process zone, which causes the supply of energy to drive the crack to occur over time rather than instantaneously, as it does in metals. Additional time dependence in the crack growth process can be due to process zone behavior, where both the flow stress and the critical crack tip opening displacement may be dependent on the crack growth rate. Instability leading to slip-stick crack growth has been seen to be the consequence of a decrease in the critical energy release rate with increasing crack growth rate due to adiabatic heating causing a reduction in the process zone flow stress, a decrease in the crack tip opening displacement due to a ductile to brittle transition at higher crack growth rates, or an increase in the rate of fracture work due to more rapid viscoelastic deformation. Finally, various techniques to experimentally characterize the crack growth rate as a function of stress intensity have been critiqued. Key words: fracture, fracture mechanics, polymers, viscoelastic crack growth 1. Introduction The subject of slow, stable crack growth in polymeric materials is growing in importance. The use of plastic pipe for natural gas and water distribution and for transport of raw sewage has become quite common during the past 15 years. Such applications are made with the expectation of service lifetimes of at least 30 years. However, such lifetimes under service conditions of constant stress, due to ground loading and internal pressure, will require polymeric materials with a high resistance to slow, stable crack growth, sometimes called static fatigue. In metals at above half of their melting temperature (expressed in degrees K), time dependent plastic deformation at the tip of cracks can result in stable, time dependent crack growth, usually referred to as creep crack growth. For most met- als, neither creep deformation nor creep crack growth is significant at ambient temperature. On the other hand, many polymers experience considerable creep at room temperature, especially for long term service. This is a consequence of the fact that ambient temperature is a significant fraction of the glass transition tem- perature (again, expressed in degrees of absolute temperature) for most polymeric materials. This creep, which results from the viscoelastic character of polymeric 242 W. BRADLEY ET AL. materials, can also give creep crack growth, or more appropriately, viscoelastic creep crack growth. The usual mechanical properties that are measured in materi- als characterization such as loss modulus, storage modulus, tensile yield strength and ultimate elongation may not be very useful in predicting a polymer’s resistance to viscoelastic crack growth. Thus, new approaches are being developed to better predict a polymer’s resistance to viscoelastic creep crack growth for engineering applications and materials development The susceptibility of polymers to viscoelastic creep crack growth has resulted in some rather expensive lessons in service. For example, it has been common in the United States for polyethylene pipe used for city distribution of natural gas in a metropolitan area to be pinched clamped to stop gas flow and allow repairs to be made. This practice makes it possible to install natural gas distribution systems in metropolitan areas with a minimum of valving compared to distribution systems made with cast iron pipe. It has been assumed that the polyethylene can be pinched clamped without introducing any damage to the pipe. However, it has been found that pinch clamping may introduce damage in the form of surface cracks at the inside diameter of polyethylene pipe that will subsequently have viscoelastic creep crack growth over a period of 5–10 years before causing leaks (Jones and Bradley, 1987). The use of plastic pipe in connection with metal fittings with sharp edges to connect city water service to residential customers resulted in the initiation and propagation of viscoelastic creep crack growth, causing leaks to develop. However, the viscoelastic creep crack growth that developed where the plastic pipe was bent around the sharp corners of the fittings took several years to produce leaks. By the time the problem was identified, the improperly designed fitting had been widely used and several thousand such applications subsequently leaked, resulting in enormous replacement costs. Metal crimps used in conjunction with plastic fittings for plastic pipe for water service in residential homes have been found to produce viscoelastic creep crack growth leading to leaks, but again only after several years of service. Thus, the problem did not “surface” until the use of the crimped fittings had become widespread. Buried PVC pipe has been found to be susceptible to viscoelastic creep crack growth when the pipe is of inferior quality and/or the installation leads to excessive ground loading (U.S. Department of Transportation, Research and Special Programs Administration, 1994). However, failures in service may not occur for several years and conventional mechanical properties tests such as tensile or internal pressure tests do not always identify pipe that is susceptible to viscoelastic creep crack growth (Jones and Bradley, 1993; Richard et al., 1959; Kausch von Schmelig and Niklas, 1963). It is clear that applications of polymers involving long term loading resulting in either constant or intermittent stresses can cause viscoelastic creep crack growth. Thus, a better understanding of how to evaluate a materials resistance to viscoelastic creep crack growth and how to produce polymeric materials with a high degree of resistance to such cracking is essential to the successful retention of some existing markets and expansion into some new markets for polymeric materials. VISCOELASTIC CREEP CRACK GROWTH 243 The application of fracture mechanics to viscoelastic media goes back to the middle 1960s (Williams, 1965; Vincent and Gothan, 1966; Retting and Kolloid, 1966). Extending Griffith’s work to linearly viscoelastic materials Williams (1965) found that the crack initiation criterion depends on the loading history. Vincent and Gotham (1966) and Retting and Kolloid (1966) were among the first to note that _ the work of fracture in polymers, 2, was a function of the crack growth rate, a. Kostrov and Nikitin (1970), following the lead of Dugdale (1960) and Barenblatt (1962) for time independent materials, were the first to note that a failure zone needs to be introduced ahead of the crack if the time dependence of the fracture process is to be properly modeled. Various approaches to model the viscoelastic fracture in the process zone have been taken, depending on the assumed geometry of the process zone ahead of the crack tip and the constitutive properties for the material in the process zone. If a process zone, or failure zone, is assumed to be finite, then the constitutive properties of the material in the process zone need to be specified (Wnuk and Knauss, 1970; Knauss 1993). Alternatively, the failing material in the process zone can be rep- resented by a stress-displacement relationship for a zone of zero thickness as was done by Knauss (1970). Knauss (1970) solved the Griffith problem for an assumed finite thickness process zone assuming a linear, viscoelastic constitutive behavior for the material in the process zone and used his model to analyze center-cracked panels of Solithane 50/50. Subsequently, Mueller and Knauss (1971) studied crack propagation in a linearly viscoelastic strip. Knauss (1974) also modeled the steady- state crack propagation in a viscoelastic sheet. Thus, by the mid-seventies, Knauss and co-workers had established a framework for the linear viscoelastic fracture of polymers through the application of cohesive crack models. At the same time Knauss and co-workers were developing their theories of viscoelastic fracture mechanics, Williams and Marshall (1972–1975) put forth the idea that fracture mechanics for viscoelastic materials could be treated with an approach that is similar to the traditional fracture mechanics developed for metals by simply replacing the time independent values for modulus and flow stress with equivalent viscoelastic relaxation moduli and flow stresses. The time scale for fracture was estimated by using a Dugdale (1960) calculation of the process zone size, which was divided by the crack growth rate. Concurrent with the work of Knauss and Williams and Marshall but indepen- dently, Schapery (1975a, 1975b) demonstrated that indeed viscoelastic creep crack growth could be described using the approach developed for metals by Barenblatt (1962) with the replacement of the elastic modulus with a viscoelastic modulus. He further indicated how to determine the appropriate time at which this viscoelastic modulus should be evaluated using linear viscoelasticity. Finally, by
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