Question 5 of 9: Texture Profile Analysis and Two-Cycle Force-Deformation Behaviour

Question 5: Texture Profile Analysis and Two-Cycle Force-Deformation Behaviour (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) General food texture profile (TPA) curve. A texture profile analysis test compresses a sample twice in succession (a two-"bite" cycle) and records force against time, producing the curve below. Each compression peak gives a hardness (the peak force of that bite; Hardness\(_1\) from the first compression, Hardness\(_2\) from the second). If the probe is withdrawn quickly after the first compression, some samples resist separation from the probe, pulling the trace briefly negative — the area of that negative region is the adhesiveness \((A_3)\). The areas under the whole force-time curve for the first and second compressions, \(A_1\) and \(A_2\) respectively, give the textural parameters in formula form: $$\text{Cohesiveness} = \frac{A_2}{A_1},\qquad \text{Gumminess} = \text{Hardness}\times\text{Cohesiveness},\qquad \text{Chewiness} = \text{Gumminess}\times\text{Springiness}.$$ Springiness is the ratio of the recovered height (or time) between the two bites to the original compression displacement, and is read from the horizontal spacing of the two peaks on the same curve. Gumminess is normally reported for semi-solid foods (which do not require chewing to swallow), while chewiness — which folds in springiness — is reported for solid foods that must be chewed.

(b) Two-cycle force-deformation curve at 10% strain. Loading the sample to 10% compression traces a rising (generally curved) loading path; unloading follows a lower path back toward zero force, but — because the question specifies a small strain where the sample is not perfectly elastic on the first cycle — the unloading curve returns to a non-zero deformation (a residual "set") rather than back to the origin. The second cycle is then drawn starting from that residual deformation and, per the question's assumption that all plastic change has by then vanished, traces an almost fully recoverable loop back to (very nearly) its own starting point.

The labelled quantities are defined as:

• Stress at 10% compression — the force (or force/area) read at the peak of the loading curve, at the specified 10% deformation.
• Degree of elasticity — the fraction of the total deformation that is recovered on unloading, \(\text{Degree of elasticity} = \dfrac{\Delta L_{\text{recovered}}}{\Delta L_{\text{total}}}\); a value of 1 is perfectly elastic (no residual set), and progressively smaller values indicate more permanent (plastic) deformation.
• Mechanical hysteresis loss — the energy dissipated per cycle, equal to the area enclosed between the loading and unloading curves of that cycle (loading work minus the smaller work recovered on unloading).
• Secant modulus of deformability — the slope of the straight (secant) line drawn from the origin of the loading curve to the point at 10% compression, \(F/\Delta L\) at that point, describing the sample's overall apparent stiffness including any curvature in the true loading path.
• Secant modulus of elasticity — the same secant construction applied only to the recoverable (elastic) part of the deformation, i.e. stress at 10% compression divided by the recovered deformation rather than the total deformation.