Question:
I have a couple fundamental questions about the stress strain curve of
materials. (I am working with plastics, but even answering these
questions with metals in mind will help.)
(1) If the thickness of a material is increased, how is the
stress-strain curve affected? Does the ultimate stress change? Does
the entire curve shift?
(2) How does the stress-strain curve changes with material fatigue?
(3) Is plastic creep a form of material fatigue?
Answer:
The stress-strain curve is unaffected. Stress is a continuum concept that
is independent of size.
It is unaffected. Fatigue is more related to the type of detail one is
using, and the imperfectionsintroduced by that detail (microcracks,
geometry effects, etc.)
No. It is a consequence of the material flow properties, which become
important undersustained loading. Fatigue is more related to a varying
load, or stress range.
Under conditions of high strain cycling (strain controlled fatigue with lots of
hysteresis), the stress-strain curve can be drastically affected. Materials
are said to cyclically soften or harden depending on the effect.
I don't know that the stress-strain curve is being altered in that case. All
that's happening there is that you're yielding, and that you're on the strain
hardening branch of the virgin stress-strain curve. The intrinsic stress-strain
curve is still unaffected.
Of course, it may look different than that. If you load a steel bar to yield well
into the strain hardening range, unload it to zero strain, and then load it up
again, the bar will yield again at the stress point where you unloaded it. It then
looks like the yield stress has been raised, and it has. But the material also has
residual, or plastic, strains in it, whereas the original yield stress is reached
with zero plastic strains.
With composites, though, strength follows a Weibull distribution. As
the number of fibers increase, strength will drop a bit
(statistically, you are more likely to have weak fibers which will
fail early). Given enough samples, thicker composites will show a
lower ultimate stress than thinner samples (for the same material,
that is).
The "intrinsic stress-strain curve" is not a material property as you
seem to imply. The cyclic softening or hardening described above is
generally measured in fully reversed cycling in the the plastic range.
For engineering purposes, the concept of a universal stress-strain
curve is an adequate approximation in most cases. However, materials
- even pure metals - are a lot more complicated than that.
The problem with thinking just in terms of stress-strain is that you
are assuming that the strain alone determines the strength. The shape
of the stress-strain curve depends on temperature, strain rate and
test sample orientation. A lot of good work has been done in this
area. Search for something like state variable models for plasticity
in metals.
How do you define "zero plastic strains"? Fully recrystallized? As
received from the vendor (annealed, half hard, etc.)? After years of
service at a high temperature? The accumulated strain and stress in
the cyclic test described above will not generally correspond to any
point on a stress-strain curve from a tensile test or other test that
allows for larger strains.
I don't mean to get carried away, but I think it is important to keep
in mind the limitations of the commonly used material models.
There are essentially two stress-strain curves for each material, a
monotonic and a cyclic stress strain curve. The monotonic is
developed for a uni-axial test specimen pulled to fracture, while the
cyclic as the name implies is developed by cycling a test specimen at
various stress levels until the specimen stabilizes for each stress
level (i.e. stops cyclically hardening or softening). These points
are then connected to develop the cyclic stress strain curve. These
two curves will almost always be different. So to answer the original
question, yes fatigue loading will affect the stress strain response.
ad (1) At "Normal" ambient temperatures the thickness does not affect
the stress-strain curve - but at the socalled transition temperature
the steel turns to be "brittle" - as seen at Charpy-tests and similar.
This transition temperature is partly determined by the content of
impurities - but is also very dependent on the plate thickness.
ad (2) For elastic load cycles it does not - untill fatigue cracks
have grown so much that they change the stiffnes of the "test"
specimen - whether this is a change in material properties or in
geometry can of course be discussed.
At plastic - cyclic strain - fatigue the material will of course show
deformation hardening - almost similar to one-loading
strain-hardening.
ad (3) No. For steel we normally distinguish between plastic
deformation and creep.
Plastic deformation normally being deformation under increasing load -
and with constant volume (Poissons ratio = 0.5).
Creep being - also plastic - deformation - but at constant load and
due to elevated temperature - normally above 350 - 400 Centigrades.
Lead will creep at room temperature.
And so will many types of plastic.
