Convert loading velocity rate to strain rate on 3-point bending tests

[Efstia]

Hi,

I would like to ask if anyone knows how to convert 100 cm/sec (loading velocity) to strain rate which units are strain per second.

Thanks a lot.

 

[rb1957]

yes? not sure if there was a question there or not ...

from peak load and E (and internal stress solution) you can easily get strain, and you need time to get strain rate (at least the way we're interpreting "rate"). could they have used "peak load rate" ?

Quando Omni Flunkus Moritati

 

[Efstia]

rb1957

They used peak load rate from impact force versus time graph. Do you claim they used peak load rate to find the strain rate?

 

[rb1957]

that sounds much more reasonable (using the peak loading rate to determine the strain rate)
than the previous post (using peak load to determine strain rate)

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[Efstia]

What I have done to much their results was to calculate the peak load rate, Moment rate, stress rate. By assuming an E value , we get the strain rate. But again, my solution does not much their results.

 

[BAretired]

Stath,
Why do you have to assume an E value to calculate strain rate? It seems to me you would need to assume an E value to get the moment rate or stress rate, but not for the strain rate because E is the same for load rate as it is for strain rate.

Δ = PL³/EI
M = PL/4
f_max = PL.y/4I
ε_max = PL.y/4EI = 12Δ.y/L²

BA

 

[BAretired]

Correction: Δ = PL³/48EI

BA

 

[Efstia]

BAretired

Ok. If I consider a 3 point bending test same with the paper written by Millard et al. 2013 with a deflection rate of 0.18 mm/min which is 0.003 mm/sec:

Span of beam = 300 mm
Width = 100 mm
Depth = 50 mm

s = My/I
M = PL/4
D = PL^3/48EI

stress = E x strain

strain = PLy / 4IE

Incorporating the deflection rate 0.003 mm/sec and rearranging the deflection:

strain = ( 48EIDLy / 4IE(L^3) )= 2 x 10^-5 s^-1.

According to the paper Millard et al 2013, the strain rate is 10^-5 s^-1 which does not agree with my calculations.

Stath

 

[rb1957]

i guess to get strain from stress ... I'm guessing he doesn't have "delta" directly.

so strain rate = 12y/L^2*loading rate. it should be good for slow rates, there maybe impact effects for fast rates.

oh, I see your point (now) BA ... the relationship is only in terms of beam geometry.

Quando Omni Flunkus Moritati

 

[BAretired]

Stath,
According to my calculation,
Unit Strain ε_max = PL.y/4EI = 12Δ.y/L²
= 12*0.003*25/300² = 0.0000100 which agrees with the paper you cited.

BA

 

[Efstia]

BAretired,

You are completely right. I did use the full depth instead of diving it in 2. Thanks.

Stath

 

[rb1957]

but (from previous post) ...
load rate (mm/sec) strain rate (strain/sec) strain/load
4.23E-6 5E-6 1.2
8.46E-2 1E-2 0.12
7E2 8E-1 0.0011
1E3 1E0 0.001

assuming load rate is reported, then to have a constant ratio (inferred by the geometry constants) you'd need ...
load rate (mm/sec) strain rate (strain/sec) strain/load
4.23E-6 5E-6 1.2
8.46E-2 1E-1 1.2
7E2 8.4E2 1.2
1E3 1.2E3 1.2

although it's reasonable that for high load rates (like 1m/sec) that the strain rate is lower, possibly a thousand times lower ...

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