8 Influence of microstructure
In this part of the lecture the influence of microstructure on the mechanical response of both polymers and metals is discussed.
8.1Polymers¶
Basically we can divide polymers into two classes, i.e. amorphous and semi crystalline. Amorphous polymers, also called polymer glasses, have no regularity on the microscopic level, i.e. no crystal formation. Semi-crystalline polymers, as the name already tells us, have regularity.
This regularity has strong implications on the mechanical response.
8.1.1Amorphous polymers¶
For amorphous polymers well developed constitutive models are available capturing all observes phenomena during mechanical loading. This response is strongly affected by its molecular architecture.
Figure 8.1:(left) key features of the intrinsic mechanical response of polymer glasses; (right) influence of molecular architecture on the intrinsic mechanical response.
The 3D constitutive model presented in the lecture is in essence the application of 3D hyperelasticity, see Hyperelasticity, combined with 3D viscoplasticity, see Viscoplasticity. The model discussed needs to capture the two typical time dependencies, see Figure 8.2, i.e. ageing and deformation rate-dependence (3D viscoplasticity), as well as proper large-strain behavior (3D hyperelasticity).
Figure 8.2:(left) dependence on polymer age; (right) dependence on deformation rate.
To demonstrate the power of a good constitutive model we apply it to different loading condition, both at the macroscopic and the microscopic level.
8.1.2Semi-crystalline polymers¶
For semi-crystalline polymers we have good insight on what the key features are which govern its intrinsic mechanical response, but up to today no constitutive models are available capturing all these features. The complexity on what should be included in such a model is easily illustrated by what kind of effect processing has on the development of microstructure of one of the chemically most simple semi-crystalline polymers, i.e. Polyethylene (PE).
PE is typically used in its Ultra High Molecular Weight form (UHMWPE) in artificial joints and bearings since it displays low friction and a high wear resistance as compared to other polymers. This form of PE has besides its favorable friction and wear properties also some drawbacks when we make artificial joints. The primary reason is that UHMWPE cannot be processed via regular injection molding, which as a consequence has a negative effect on its wear resistance. By manipulating the microstructure after processing one of these drawbacks is removed, but immediately replaced by another.
Besides the lecture slides we refer the reader to Chapter 7, Mechanische eigenschappen, of the book “Polymeren van keten tot kunstof” by A.K. van der Vegt and L.E. Govaert.
8.2Metals¶
Like polymers, metals form an important class of materials. For metals the carriers of plastic deformation on the microstructural level are clearly identified in the form of dislocations, which in essence are defects in the crystalline roster. see Figure 8.3.
Figure 8.3:Imperfection in the form of an edge dislocation. Image taken from Material Science and Engineering edition.
The ease of movement of these dislocations determines the plastic deformation response. Restricting the mobility increases the tensile strength, i.e. the maximum stress reached before failure, of the material. For pure metals there are two mechanisms available to influence the mobility:
refining the grain size.
increase the dislocation density.
By decreasing the size of a grain the probability of pinning a dislocation on the edge of the grain increases significantly and therefore increases the tensile strength. The latter mechanism is explained by dislocation repulsion, see Figure 8.4. Since two dislocations of the same direction repel each other, increasing the density results in an increase in probability of two dislocations of the same direction meeting each other, thus forming a barrier for the dislocation to move.
Figure 8.4:Graphical representation of repelling and attracting dislocations. Image taken from Material Science and Engineering edition.
Two frequently used experimental techniques are available to influence the aforementioned mechanisms:
cold working, also known as strain hardening or work hardening.
annealing.
Via the first technique dislocations are created, where the latter is used to influence the size of the grains and decrease the dislocation density in the metal.
Besides the lecture slides we refer the reader to Chapter 7, Dislocations and Strengthening Mechanisms, of the book “Material Science and Engineering: an Introduction” by W.D. Callister, Jr.
8.3comparison between polymers and metals¶
In general, for both polymers and metals, an increase in (tensile) strength leads to a decrease in toughness, i.e. maximum strain at break. The Holy Grail of course is to increase both at the same time.
Where for polymers mechanical deformation leads to a decrease in yield stress (tensile strength), in a metal the opposite is observed. For annealing also an opposite effect is observed. Metals recrystallize resulting in a decrease in tensile strength, where for polymers the polymer chains move to a more favorable configuration, resulting in an increase in yield stress.