The absolute density is determined experimentally by the pycnometer method according to NF P 94-054. The procedure used consisted in carrying out the following operations:

· Select a sample and place it in the oven at 105˚C for 24 hours.

· Weigh a pycnometer filled with distilled water to the mark and note its mass M₁.

· Weighing a sample of aggregate of mass M₂.

· Introduce the sample into a pycnometer after pouring in a quantity of water.

· Gradually fill the pycnometer up to the mark, eliminate air bubbles and note M₃ its mass.

· Note the temperature of the water in the pycnometer.

The values of the individual weights are used to determine the absolute density.

ρ a b s = ρ e ⋅ M 2 / [ ( M 1 + M 2 ) − M 3 ] (1)

where ρ e is water density taken conventionally

The bulk density was determined by the hydrostatic balance method according to the recommendations of NF P 94-053. The principle of the method consists in determining the volume of a sample by means of the Archimede thrust. It is obtained from successive weighing of the sample. Samples are taken by the quartage method and weighed on a 10⁻³ g precision scale.

· Let methe mass of the sample, then the sample is immersed in previously melted paraffin.

· Let m_e+p, the mass of the sample plus paraffin (with a density of 0.87796 g/cm³)

The wax sample is then carefully immersed in water.

o The displaced volume of water V_d is given by the expression V d = V e + V p

o The volume of the paraffin is: V p = m e + p − m e ρ p

o The volume of the sample is given by the relationship V e = V d − V P

The bulk density is expressed as the ratio of the mass of the sample to the volume of the sample.

ρ a p = m e V e (2)

The palm kernel shell has geometry similar to that of the globe, i.e. it has two poles and meridians. To test the isotropy hypothesis, we propose to take samples in the Meridional direction and the Equatorial direction as shown in Figure 1.

We took the PKS DURA and TENERA specimens in the southern and equatorial directions. The aim was to see whether its mechanical characteristics vary according to the orientation in which the specimen was cut, in order to ensure the isotropy of this material. Table 1 represents the orientation M and E adopted; we have chosen a set of 20 specimens.

We determined it experimentally using the Charpy’s Sheep method using a pendulum sheep adapted to plant shells, carried out at the LAMMA laboratory of ENSET, Douala as shown in Figure 2.

R = m g l ( cos θ − cos θ 0 ) S (6)

with l: length of the pendulum arm (320 mm);

m: mass of the pendulum arm;

θ: angle of ascent after specimen breakage;

θ₀: angle of free upward movement;

g: acceleration of gravity at the test site;

S: cross-section of the test specimen.

Influence of temperature on impact energy

This influence has been assessed by impact tests on specimens subjected to temperatures ranging from 26˚C to 90˚C. For each temperature range, seven specimens were tested. The temperatures were measured using a type K thermocouple.

Due to the curved geometry, PKS does not offer the possibility to obtain straight specimens for the classical uniaxial tensile test; we will limit ourselves to three-point bending and elastic contact tests. The deformation energy will allow us to establish an equation whose parameters will be E and ν. We will take the fish coefficient value of 0.4 because palm kernel shells are similar to wood.

1) Principle of the three-point bending test

The bending test shall be carried out on a specimen in the form of a portion of a cylinder. This test piece is comparable to a curved beam whose mean line is in the form of an arc of a circle. We tested 20 specimens in the southern and equatorial directions. Figure 3 below shows the boundary conditions.

We place specimen (4) on the supporting surface integral with the frame (5), the end of the slide (2), bearing a steel ball is positioned at point C of the shell. The masses (1) are placed above a plate attached to the slide. The feeler of the dial gauge (3) is located under the shell and is used to directly measure the deflection corresponding to a given load in the extension of the slide rail. Several pairs of data (load, deflection) can be collected in the elastic range.

2) Mathematical expression of the deflection-load relationship

The application of Castigliano’s theorem will allow us to establish a linear

relationship P = α∙Y_c with P the load applied at point C, Y_c the deflection at point C andα the slope of the straight line which is a function of the static Young’s modulus, the fish coefficient and the geometric dimensions of the specimen.

3) Expression of the deformation energy of a specimen

The total deformation energy U is due to internal forces [10] [11] [12] [13] is described by Equation (7) and given by Equation (8).

U = 2 ( U 1 + U 2 + U 3 ) (7)

with U₁ = Deformation energy due to normal effort N

U₂ = Deformation energy due to sharp effort T_R is negligible

U₃ = Deformation energy due to flexural moment M_fz

U = 2 ( U 1 + U 2 + U 3 )     or     U 2 = 0 ⇒ U = 2 { R P 2 16 E S [ π 2 − θ 1 + 1 2 sin ( 2 θ 1 ) ] + P 2 R 3 8 E I G z [ ( π 2 − θ 1 ) cos 2 θ 1             − 2 cos θ 1 + 3 4 sin 2 θ 1 + 1 2 ( π 2 − θ 1 ) ] } (8)

L and e are the dimensions of the cross-section S.

E is the static Young’s modulus in longitudinal direction.

P is the applied load.

I G Z = 1 12 × L e 3 is the quadratic moment of the straight section.

The application of Castigliano’s theorem to the midpoint of the specimen C allows us to write Y c = ∂ U ∂ P we thus obtain the relation below:

Y c = ∂ U ∂ P

⇒ Y c = { R 4 S [ ( π 2 − θ 1 ) + 1 2 sin 2 θ 1 ] + R 3 2 I G z [ ( π 2 − θ 1 ) cos 2 θ 1                         − 2 cos θ 1 + 3 4 sin 2 θ 1 + 1 2 ( π 2 − θ 1 ) ] } × P E (9)

Let’s pose

β = R 4 S [ ( π 2 − θ 1 ) + 1 2 sin 2 θ 1 ]           + R 3 2 I G z [ ( π 2 − θ 1 ) cos 2 θ 1 − 2 cos θ 1 + 3 4 sin 2 θ 1 + 1 2 ( π 2 − θ 1 ) ] (10)

Substituting Equation (10) into Equation (9), gives Equation (11)

Y c = β × P E (11)

The factor β depends on the geometrical characteristics of the specimens. From expression P Y c = E β ; E is determined. The slope P/Y_c has been obtained experimentally as the slope of the linear regression.