Mechanical Properties of Materials and Testing Methods

ANSWER SHEET
MECHANICS SECTION
1) Stiffness- The magnitude of resistance to deformation when an object is subjected to
external forces (either in tension or compression). The greater the resistance to
deformation the greater is the stiffness of material. Different materials exhibit different
stiffness ranges.
2) Elastic modulus- This refers to the ratio of stress (applied on a body of an object) to the
produced strain within the elastic region (the elastic region is the portion where material
regains its original length when the stress causing the strain is released).
3) In mechanical property, is mostly defined as response obtained from mechanical loading
in a material; often depends on the material structural property while in structural
property, this is the inherent characteristics present in a material and is often independent
of mechanical property (Bilandzic and Stenvers, 2011)
4) We know that from Hooke’s law:
F= ke where e= extension and k= stiffness of material
From the definition of elastic modulus above, E= Г/έ only for isotropic materials
But έ=e/L such that e=έ/L.....(i)
From F=ke ; e= F/k .....(ii)
Equating the two equations: έ/L= F/k
έ=FL/k...(iii)
Alternatively, from the definition of elastic modulus: E= Г/έ

And we also note that : Г=F/A
Therefore, E= F/A/έ=F/Aέ
Which implies that : F= AέE
And from Hooke’s law: F=Ke
Equating these two equations: eK= AέE
Hence K= AEέ/e....(iv)
Equations (iv) and (iii) should be equivalent as far as relations between k and E is
concerned hence: K= AEέ/e or έ=FL/K
5) (a) The maximum stress Гmax= Fmax/A
From the given figure, Fmax= 6.5N
Now, cross sectional area of an elliptical solid/surface is given by: A= πab where a=semi-
minor axis radius and b=semi-major axis of radius
a= 0.75/2 and b= 2/2=1
A= 3.142 x0.75/2x 1= 1.17825mm2
Гmax= 6.5/1.17825x10-6 = 5.517MPa
(b) Maximum strain, έ=e/L= 1.2/8= 0.15
(c) Linear regression elastic modulus
E= Г/έ= 5.517MPa/0.15= 36.78MPa
(d) For this case, we consider the limit state fixed at 2% for Toe region in most
biomaterials

2% offset
6) It is imperative to report both since the toe region indicates the correction factor that is
due to material set up alignment. Normally, there will be experimental error attributable
to the set up for example slipping of jaws. Therefore, this parameter is normally used to
make corrections based on these circumstances (Kirkbride, Townsend, Bruinsma,
Barnett, Blobe, 2008)
7) (a) Compression cycle
(b) –cartilage
-collagen
-Ligament
(c)(i) Collagen
(ii) Proteoglycan
(iii) Chondrocytes

8) Anisotropy refers to the tendency of a material exhibiting different physical behaviors
along different orientations (Schäfer and Radmacher, 2005). In other words, the term is
used to describe the material behavior to have different properties in different directions
such that if tests are conducted laterally and transversely in the same material, different
results are obtained. For example, the strength characteristics of such a material will often
vary from direction to direction. In one direction, it may be stronger and in the other
direction it becomes weaker. A good example is wood; based on the grain orientations, it
is easier to split wood along the grains but not across the grains.
9) Poisson’s ratio normally describes a material such that the length is increased while girth
decreases in a pure tension force application. Therefore, a Poisson’s ratio of 0.5 indicates
that the material is perfectly incompressible and elastic (Fictiv.com, 2018 and Yamamoto
and Nakamura, 2017). In other words, in Poisson’s ration, as the length is increased by a
factor say 2, the girth decreases by the same factor while volume of material remains
constant. The reverse is normally true; in compression tests, the girth will increase while
the length decreases. Therefore, Poisson’s ratio indicates the extent in which change in
length affects the girth of a material.
10) It will stay the same since there is neither addition nor extraction of material. Besides,
volume changes are often influenced by either thermal expansion or contraction.
Temperatures remain constant. The parameters that are likely to change are the length
and diameter and this occurs in equal proportion (Bilandzic, Wang , Ahmed , Luwor ,
Zhu, Findlay, 2014).