El Programa Estratégico de Articulado Nutricional en el Perú

In creep testing the sample experiences a sudden change in the shear stress im posed w ith the resulting tim e-dependent shear rate being m easured. It is valuable both theoretically and practically to consider a system in the rheological ground state, that is w ithout the m ethod of testing significantly altering the structure. This enables fundam ental param eters like elasticity and viscosity to be estim ated.

M ost of the instrum ents used in creep w ork operate on a sim ilar principle. The sample is loaded betw een two cylinders or plates of a therm ostatically controlled viscometer. The m aterial is then left to rest for a suitable length of time to allow all stresses in the m aterial to relax. A torque is then applied to the inner cylinder or one plate and the resulting small m ovem ent is recorded by a device like a displacem ent transducer, the output from which is then fed to a recorder. Instantaneous delivery of torque to the cone or cylinder m ay be achieved by the use of an electrom agnetic release m ech an ism .

W arburton and Barry, (1968) used a m odification of the W eissenberg Rheogoniom eter for creep w ork in w hich a chemical balance was used to apply a torque. W hen the balance arm was raised, a force equivalent to the mass in the pan was delivered to the inner cylinder. The resulting m ovem ent was m easured using a displacem ent transducer which was attached to the cylinder by means

of a 10cm arm. Barry, (1974) describes a sim ilar instrum ent w hich has an air turbine to centre, support and drive the inner cylinder. The constant stress rheom eter was also used by Davis et al. (1968) for both continuous shear and creep work.

The parallel plate system em ployed in the m ore m o dern in stru m en ts, (such as the Carri-M ed CSL used for this study), provides a convenient m easuring system for stiff m aterials, and the gap can be adjusted to overcome any clogging problem s and to increase the strain sensitivity of the instrum ent. The Carri-M ed CSL has a w ide shear rate and stress operating range which makes it very suitable for creep m easurem ent.

1.3.9.1 ANALYSIS OF THE CREEP CURVE

In creep m easurem ent the sample is treated as if it w ere an elastic solid. The stress is applied and the deform ation that results is recorded. The ratio of the stress to the shear rate is the N ew tonian viscosity, if the sam ple is a N ew tonian fluid. If the sam ple is not N ew to n ian , b u t incorporates a viscoelastic stru ctu re then the deform ation of the structure is characteristic and can be deduced from the curve of strain against time. Creep analysis m ust be carried o u t in the linear region, and the m aterial should be in the com pletely relaxed state before any stress is applied. In order to apply the theory of linear viscoelasticity to the creep test, the strain response m ust be proportional to the applied stress, i.e., stra in /stress = compliance (J), and is a constant. The creep compliance, J (t) is defined by;

J (t) = Y ltl (1.10) o

w here Y (t) is the shear strain after time t, and a = shear stress. A plot of J (t) versus time as show n in Figure 1.8 is know n as a creep com pliance curve. The same curve is produced regardless of the m agnitude of the applied stress, provided the test is ru n in the linear viscoelastic region.

A

LU

ü

Z

<

û.

o

ü

T I M E

Figure 1.8 Typical Creep Compliance and Recovery Curve for a Viscoelastic Material (Sherman 1970).

(1) A - B is the region of instantaneous compliance in w hich bonds betw een the prim ary structure units stretch elastically.

Jo = _I_ = Yo (t) (1.11) Go a

w here Gq = instantaneous elastic m odulus, Yo (t) = instan tan eo u s strain at time zero, a is the applied shear stress.

(2) B - C is the time dependent elastic region w ith a compliance Jr . The slope of the linear p art of the curve gives the inverse of the retardation time. The intercept of the extrapolated linear region on the axis gives Ji, the creep compliance.

(3) C - D is the linear region of N ewtonian compliance, Jn.

(4) D - E is the region of instantaneous elastic recovery as is of the same m agnitude as A - B.

(5) E - F is the region of retarded elastic recovery which is equivalent to B - C of the up curve.

As bonds w ere irreversibly broken in the C - D region of the curve, this part of the structure is not recovered and is represented by F - G.

The analysis of the creep curve fron the C arri-M ed CSL divides the analysis into an exam ination of the retard atio n and relaxation times. The structure of a sample can be described in term s of springs to represent elastic behaviour and dashpots to denote viscous, flow ing behaviour. The structural inform ation obtained by this technique can be directly related to the bonds and m echanism s w hich operate in the test sample. W hen the stress is initially applied to the sam ple there is an im m ediate deform ation d u e to the u n d am p ed elastic behaviour and the sample is described in term s of the num ber of viscoelastic Voigt units fitted. The rate at an d the extent to w hich an individual Voigt unit m oves d ep en d s on the

dam ping effect of the dashpot and the strength of the spring, i.e. its rigidity m odulus. The ratio of these is called the retardation time. Once equilibrium is reached, initially by the spring and dashpot w ith the shortest retardation time, m ovem ent ceases. Voigt u n its w ith lo n g er reta rd atio n tim es continue to m ove u n til finally all m ovem ent ceases. Therefore the Voigt units reach equilibrium in ascending order of retardation times and as the analysis proceeds the m ovem ent or compliance of each Voigt u n it is overlaid by the compliance of the Voigt unit w ith the shorter retardation time. The com puter data analysis characterizes the curve by m easuring the initial compliance at the bottom of the curve, the viscosity at the top, and then fitting a num ber of exponential expressions, as the behaviour of a single Voigt unit is exponential.