Should the Youngs Modulus increase or decrease? 2

[bojoka4052]

I have a concrete sample (preloaded), which has an initial Youngs Modulus (E). It is then loaded and unloaded several times. As you can see on the curve below the stress-strain relationship becomes nonlinear; should one not expect the Youngs modulus to be reduced? Reading previous notes it seems to think the youngs modulus increases the more times its loaded/unloaded.

 

[le99]

I think you can take note from the graph that the stresses are almost constant but the strain continues to increase. Doesn't it tell something?

 

[bojoka4052]

E = stress/strain, so stress is constant but strain increases, hence the youngs modulus should decrease is what im thinking. Is this wrong?

 

[rb1957]

you're using a too simple approach to Young's modulus.

a better description is E = d_stress/d_strain (ie the slope of the streas strain curve).

what your data is showing is there is hysteresis in the stress/strain relationship, typically called work hardening.
you can see this by overplotting the loading cycles.


another day in paradise, or is paradise one day closer ?

 

[centondollar]

Reading what "previous notes" do you arrive at the conclusion that young´s modulus is increased for a concrete sample loaded repeatedly? I urge you to pick up your textbooks from school and read about how Young´s modulus is defined for small strains and displacements.

Furthermore, if stress is constant but strain increases (which does not happen in reality, by the way: ideal plasticity is only a mathematical construct), the slope (giving the tangent elastic modulus) is clearly zero, and therefore stiffness is zero.

The blue curve in your figure seems to illustrate a non-linear (approximately parabolic) stress-strain relationship (and therefore a nonlinear stiffness) until unloading, and that during repeat loadings, there is irrecoverable plastic strain and stress (neither stress nor strain return to zero after unloading), but almost no change in stiffness during the repeat loading cycles. Please note that your figure looks odd: it is not typical for stress to remain non-zero in concrete after unloading, which indicates that the cyclic loading in question did not include a complete removal of load at any point during the experiment.

As rb1957 also mentioned, non-elastic hysteresis is also present.

 

[rb1957]

I wonder if it was a displacement controlled not a load controlled) test ?

another day in paradise, or is paradise one day closer ?

 

[HTURKAK]

This is cyclic loading and the max . stress level less than ultimate strength. When you look local modulus of elasticity, ( the local slope of slope of the stress strain curve ) may increase... If the stress level reaches ultimate strength , the following stress strain curve will develop ..Notice that the envelope to this curve is close to the stress–strain curve for a monotonic test.

The following Snap is from Reinforced Concrete Mechanics and Design ( J.Wight )

I will suggest you to look to the following doc.

 

[rb1957]

is that "stress-strain curve for monotonic loading" for load over time ... like a load of 2000 will (over time) cause a strain of 0.006 and fail the structure ?

another day in paradise, or is paradise one day closer ?

 

[dik]

HTURKAK... you never fail to amaze me...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[bojoka4052]

So E = d_stress/d_strain (ie the slope of the stress strain curve), meaning the greater the slope the higher E will be. In the figure HTURKAK posted I can see some places where the slope increases in the next "cycle", but generally it seems as we get more and more cycles the slope decreases substantially?

 

[DrZoidberWoop]

Look up "continuum damage mechanics" if you want to 1) thoroughly understand the constitutive relationships between stress & strain or 2) quickly learn how terrible you are at math and safely retreat back to our happy little simplified design world.

σ = (1 − ω)Eε
ω = damage variable: there are as many equations for this as there are published authors in the field.