Methodological Aspects of Determining Apple Mechanical Properties During Impact

Figures & data

FIGURE 1 A: A typical course of the sample force response recorded in the sensors installed in the hammer and anvil during the impact; B: The way of determining time between the beginning of the force response increase in the sensors installed in the hammer and anvil.

TABLE 1 The value ranges obtained experimentally

Variable	Mean	Minimum	Maximum
Fhmax (maximum force response on the hammer, N)	75.9	18	168
σf (failure stress, MPa)	0.4	0.196	0.612
εf (failure strain, –)	0.049	0.033	0.07
Δl (displacement corresponding to Fhmax, mm)	0.927	0.622	1.367
vw (shock wave speed, ms^–1)	292	163	486
ei (impact energy, J)	0.032	0.0057	0.092
eab (absorbed energy, J)	0.0032	0.0004	0.008
E (secant modulus, MPa)	8.45	3.5	13.6
k (stiffness, Nmm^–1)	83.9	16.7	203.2
T (tissue toughness, MPa)	0.0085	0.0035	0.0142

TABLE 2 The correlation coefficients for all independent and dependent variable pairs

Variable		v	l	d	Fhmax	σf	εf	Δl	vw	ei	eab	E	k	T
v	1		0	0	–0.04	–0.06	0.57*	0.51*	–0.28*	0.05	0.07	–0.35*	–0.14*	0.14*
l			1	0	0.06	0.21*	–0.08	0.46*	–0.15*	0.21*	0.20*	0.13*	–0.10	0.16*
d				1	0.95*	0.26*	0.32*	0.31*	0.05	0.90*	0.90*	–0.04	0.91*	0.51*
Fhmax					1	0.50*	0.29*	0.31*	0.05	0.95*	0.94*	0.12	0.94*	0.63*
σf						1	0.06	0.15*	–0.07*	0.48*	0.46*	0.56*	0.40*	0.73*
εf							1	0.85*	–0.24*	0.45*	0.42*	0.46*	0.13*	0.51*
Δl								1	–0.27*	0.53*	0.50*	–0.32*	0.07	0.54*
vw									1	–0.11	–0.06	0.10	0.13*	–0.16*
ei										1	0.98*	0.05	0.82*	0.75*
eab											1	0.05	0.81*	0.71*
E												1	0.28*	0.20*
k													1	0.49*
T														1

*denotes statistical significance on the level 0.05.

TABLE 3 The multiple regression models

General form of the model: dependent variable = A0 + A1v + A2l + A3d
Dependent variable	A0	A1	A2	A3	R^2
Fhmax	–106	–0.04	0.067	0.952	0.91
σf	0.183	–0.06	0.215	0.262	0.11
εf	0.038	0.58	–0.09	0.327	0.44
Δl	–0.221	0.507	0.451	0.315	0.56
vw	415	–0.28	0.08	–0.09	0.09
ei	–0.089	0.042	0.205	0.898	0.85
eab	–0.009	0.076	0.212	0.908	0.86
E	7.44	–0.35	0.133	–0.04	0.143
k	–2.92	–0.14	–0.1	0.913	0.86
T	0.0005	0.15	0.165	0.51	0.3

FIGURE 2 The influence of the impact velocity, the sample length and diameter on the failure stress and strain for the “Braeburn” variety apple flesh.

FIGURE 3 A: The mean values of the shock wave speed for different impact velocities, sample lengths and diameters; B: The percentage contribution changes of the absorbed energy e_ab to the impact energy e_i depending on the impact velocity and the sample length and diameter.