Question

What do isodeformation conditions in composite materials mean and describe the rule of
mixtures for binary compounds.

Answer 1

Solution:

(a)iso-deformation of a composite material;

Composite material:

The term composite is typically applied to a material when the multi-phase structure is constructed by direct intervention
Composite Material Examples: glass fiber reinforced plastic (GRP), wood, clam shell, Mars bar.
Multi-phase Material Examples: precipitation strengthened aluminum alloys, Ti-6Al-4V, dual-phase steel, transformation toughened alumina (Al2O3-CeO2)
Iso-deformation:

(a)iso-stress:

As implied, iso-stress means same stress in all materials; iso-strain means same strain in all materials.
For iso-stress you can think of the phases as being connected in series between the planes across which the load is transmitted (and vice versa for iso-strain).
“Iso-” is a prefix meaning “same”. Deformation is an assumption that the phases experience the same stress.
By contrast, isostrain makes the assumption that the phases are subject to the same strain.
Each assumption leads to very different results, especially when the properties of each phase are divergent, as we see from the example of the brick and the foam.

strain:

Imagine parallel slabs of material between platens that apply a load.
Phase A has volume fraction VA and modulus EA; Phase B has volume fraction VB and modulus EB.
We assume isostrain because each phase sees the same change in length.
The strain, c, is therefore the field; the stress is the response (and the stiffness is the property).
2.Rule of mixtures:

What is the simplest model that can be used to predict a material property in a composite? Answer: Rule of Mixtures
Define the volume fractions, V, of the various materials comprising the composite. The average property of the composite is then given by, discrete:
PC = VAPA + VBPB + … = S ViPi continuum: PC = ∫ P(x)dV
The Rule of Mixtures is an acceptable first approximation for estimating composite material properties. It is, however, often considerably in error and better methods are required.