A Computer Aided Characterization of the Compressive Creep Behavior of Potato and Cheddar Cheese S. PURKAYASTHA, M. PELEG, E. A. JOHNSON, and M. D. NORMAND ABSTRACT Compressive creep curves of potato flesh and cheddar cheese were fitted by a modified, four parameter model of the kind J(t) = K, + Kit + t/(K2+Kst) where J(t) is the compliance and the K’s charac- teristic constants. The curves were fitted both with and without cor- rection for cross-sectional area expansion and the nonlinearity of the strain. The fit of the model was comparable to that of the dis- crete Kelvin-Voigt model with 4 or 6 constants. The magnitude of the modified model constants was indicative of the general rheo- logical character of the material and the stress dependency of the nonlinear viscoelastic behavior. INTRODUCTION ONE OF THE MANIFESTATIONS of viscoelastic materials is that they undergo creep, i.e. continue to deform under constant stress or load. The distinction between constant stress and constant load (force) is necessary, especially for highly deformable foods, because of the progressive change of the specimen’s cross-sectional area. Thus, a constant load (i.e. dead weight) produces a progressively increasing stress in uniaxial tension and decreasing stress in compression. The typical shape of a creep curve is shown schematically in Fig. 1. In many cases, especially in tension, the test ter- minates with the failure of the specimen. In most rheolog- ical analyses, however, this stage is intentionally avoided by regulating the magnitude of the imposed load. Quantifica- tion of the creep behavior of solid food materials has tradi- tionally been based on linear viscoelastic models primarily of the generalized Kelvin-Voigt type with a discrete num- ber of elements (e.g. Morrow and Mohsenin, 1966; Shama and Sherman, 1966; Sharma and Mohsenin, 1970; Mitchell and Blanshard, 1976a, b; Reidy and Heldman, 1972; Wang and Chang, 1970; Gross et al., 1980; Datta and Morrow, 1983). In all these cases, the creep equation is of the general form : J(t) = K. + Kr t + !Z Kl[ l-exp(-t/71)] i=2 (1) where J(t) is the compliance (i.e. strain per unit stress), the K’S are constants and the 7i’s are time characteristics or retardation times. It was demonstrated by the various reports that for fit- ting individual creep curves, the number of constants re- quired (i.e. K’s and 71’s) was generally between 3 and 12. Other investigators have tried to account for the non- linear behavior of foods either by incorporating a St. Venant element into the model array (e.g. Lasztity, 1980; Chuma et al., 1978) or by substituting a set of polynomial equa- tions (Sharma and Raffie, 1983) for Eq. (1). It ought to be mentioned at this point that nonlinear viscoelasticity is not necessarily expressed in the goodness of the fit of linear models. As a matter of fact, it can be shown that individual creep curves, i.e. the relationship between J(t) and t shown in Fig. 1, can always be fitted by a mathematical expression Authors Purkayastha, Peleg, Johnson, and Normand are affiliated with the Dept. of Food Engineering, Univ. of Massachusetts, Am- herst, MA 0 1003. of the type expressed in Eq. (1) provided there is no restric- tion on the number of exponential terms. Nonlinearity, therefore, will mainly be evident from the fact that the equation’s coefficients (i.e. the K’s and r’s) are not constants but functions of the imposed stress. Another feature of nonlinear behavior in creep (see Fig. 2) is that the magni- tude of the instantaneous compliance in loading (KoL) is different from that of the instantaneous compliance in re- covery (KoR), but this aspect will not be discussed in the present work. It should also be added that, theoretically, a true solid material reaches equilibrium creep strain (or compliance), especially in compression. In terms of Eq. (l), this will be Jo INSTANTANEOUS COMPLIANCE J,’ K, E;K; J,(t)1 STEADY STATE FLOW WI THE CREEP FUNCTION CKi OR 1/K; ---- t 2/K; J(t)1 THE CREEP CURVE Ko=K; - TIME (t) ----) Fig. l-Schematic diagram of creep compliance curve and its three components as described in Eq., (1). (J(t) is the total compliance and K, K 1, K-7 and K3 are constants), Volume 50 (1985)-JOURNAL OF FOOD SCIENCE-45