Loading History Effects on the Creep and Relaxation Behavior of Thermoplastics

Abstract

Experimental investigations have been performed to understand the effects of prior loading on the creep and stress relaxation behavior of an amorphous polymer (polyphenylene oxide) and a semi-crystalline polymer (high density polyethylene) at room temperature. Of particular interest was the positioning of creep and relaxation tests on the unloading segment of stress-strain curves for tensile and compressive loading. The data was found to be quite unlike that obtained in typical tests performed on the loading segment; i.e., with no unloading history. Specifically, in relaxation tests, rather than registering a monotonic drop, the stress first increases then decreases. The rate of change of stress, therefore, is initially positive and then becomes negative. Similarly, in creep tests, the strain was found to decrease at first, and then began to increase. This has been labeled as rate-reversal in the context of relaxation and creep test data, and, furthermore, the test point has been found to influence the stress-time and strain-time data, respectively. In relaxation, for instance, at large strain values, the initial increase in stress is considerably smaller than the subsequent drop and the rate reversal occurs very rapidly. Conversely, at smaller strain values, the initial increase in stress dominates and the rate reversal may occur only after several hours. Analogous changes are observed during creep as tests are performed at lower stress values. Preliminary attempts at modeling the aforementioned creep and relaxation behavior have been made by modifying the existing formulation of the viscoplasticity theory based on overstress, which is a constitutive state-variable based model. A modified, single-element standard linear solid serves as a suitable descriptor of the model. Linking of two elements in series has shown some promise towards the modeling of the rate-reversal behavior. Experimental data and results of preliminary simulations are presented in this study.

Experimental investigation and modeling of non-monotonic creep behavior in polymers

“…3, which illustrates creep at 8 MPa, the strain first decreases, then registers an increase in magnitude. A somewhat similar and equally singular response has been reported earlier by Khan (2006) and Zhang and Moore (1997) in the case of relaxation with a prior loading history comprising of loading and partial unloading, but in these cases the stress during relaxation is observed to decrease and then increase during relaxation. Increasing strain at high stress levels and decreasing strain at low stress values during creep in Type III test conditions have also been experimentally observed by Khan and Farrokh (2006).…”

“…For example, an ultra high molecular weight polyethylene (UHMWPE) load bearing insert in a prosthetic joint might see high levels of loading during activity such as stair climbing which is followed by partial unloading as the individual stands still. This behavior has been reported by the PI, Khan (2006), Zhang and Moore (1997), Hamouda et al (2007), and Falcone and Ruggles-Wrenn (2009). The originality of the scientific contribution made by this paper stems from an account of the modification to the VBO model to better capture the curved unloading segment of a polymer's stress-strain curve, and by furnishing a quantitative juxtaposition of model and experimental data to establish the model's competency at capturing rate reversal in creep.…”

“…A preliminary approach to the modeling of stress relaxation exhibiting a decrease, increase, or a combination of a decrease followed an increase in stress, is presented in Khan (2006). This formulation has been used again to verify the ability to produce non-monotonic strain-time behavior in creep which has been established with experimentation on UHMWPE and polycarbonate (PC) specimens.…”

Time-dependent response of polypropylene after strain reversal

“…Similar phenomena were also revealed in creep tests. Changes in shapes of relaxation and creep curves with D were also reported by Zhang and Moore (1997), Khan (2006) for high density polyethylene and Kim and Sun (2002) for a polymer composite. Evolution of shapes of relaxation curves was called ''anomalous" (Kitagawa et al, 1999) or ''unusual" (Heymans and Kitagawa, 2004) behavior after strain reversal.…”

“…A shortcoming of this concept is that it requires the equilibrium stress r eq to evolve with time in order to capture mixed relaxation. Although it is possible to describe the non-monotonic dependence of stress on time within the VBO theory (Khan, 2006), such a model involves a number of merely phenomenological relations and ensures only qualitative agreement with observations (Kitagawa et al, 1989;Sanomura and Mizuno, 2007).…”