I have results from a load-deflection curve that behaves non-linearly. I need to convert this to a stress-strain curve and/or find the final Modulus of Rupture (MOR).
To do so, converting the deflection into strain is possible as per ASTM D790
εf = 6Dd/L^2, where D is the maximum deflection, d is depth and L is the span length.
I would like to convert the load to stress as well, however, the conventional equation from beam theory is not applicable past the yield point,
σf = 3PL/2bd^2, where P is the load.
I'm aware that it somehow involves the neutral axis and the modified I (moment of inertia) but struggling to make sense of it. The end goal is to find the MOR.
Any help about this is appreciated :)
To obtain a stress-strain curve from a nonlinear or elasto-plastic load-deflection curve in a 3-point bending test, you can follow these general steps:
It's important to note that the specific approach and techniques for obtaining a stress-strain curve will depend on the characteristics of the material, the available data, and the analysis requirements. It may be beneficial to consult relevant literature, experimental standards, or seek guidance from experts in material testing and characterization to ensure accurate representation of the material's behavior.
Hi Yousef Bahrambeigi
I appreciate your response.
The issue is with point #5, calculating stress (= Mc/I) from the bending moment and section geometry is only applicable until the point of proportionality. It's not applicable after that.
I'm seeking advice on calculating stress after that point, which will then assist me in calculating the bending capacity. Hope it makes sense.
Once again, thank you for your response.
Hi Janeshka Goonewardena,
In my opinion, to reconstruct σ-ε diagram from known load-deflection curve is a kind of inverse problem. Generally speaking, such problems are ill posed. You can proceed from some particular approximation of σ-ε diagram (for example, bilinear), find the solution of direct problem (load-deflection curve) and then vary the parameters of σ-ε diagram to find those that give a minimum deviation (eg, the mean square) of load-deflection curve from the experimental one.
Hi Victor J. Аdlucky
Thank you for your response. This confirmed my speculation as well.
Thank you for taking tithe me to respond to this and my messages.
Hi
When dealing with non-linear load-deflection curves in a three-point bending test, converting the load to stress can be challenging, especially beyond the yield point. This is because conventional beam theory assumptions, such as linear elasticity and plane sections remaining plane, are no longer valid in the plastic deformation region.
To estimate the stress-strain relationship and determine the Modulus of Rupture (MOR), you can use an alternative approach called the "Secant Modulus Method." Here's a step-by-step guide:
It's important to note that the secant modulus method provides an approximation of the stress-strain relationship beyond the yield point. For more accurate results, you may need to consider more advanced material testing techniques or consult specific standards and guidelines relevant to your material and test method.
HI VAIBHAV KUMAR MISHRA
In my opinion,
To obtain a stress-strain curve from a nonlinear or elasto-plastic load-deflection curve in a 3-point bending test, you'll need to follow these general steps:
Keep in mind that obtaining an accurate stress-strain curve from a load-deflection curve can be challenging, especially for nonlinear or elasto-plastic materials. It requires careful consideration of factors such as material properties, specimen geometry, and the specific behavior of the material under load. Advanced testing techniques and analysis methods, such as digital image correlation or strain gauges, may be required for more accurate measurements in such cases.
hi
The first step is to convert the deflection into strain. You can do this using the equation you provided:
εf = 6Dd/L^2
where:
- εf is the final strain
- D is the maximum deflection
- d is the depth of the specimen
- L is the span length
Once you have the strain, you can convert it to stress using the following equation:
σf = Eεf
where:
- σf is the final stress
- E is the elastic modulus of the material
The elastic modulus is a material property that is typically provided by the manufacturer.
The conventional equation from beam theory is not applicable past the yield point because the material is no longer behaving elastically. After the yield point, the material begins to deform plastically, and the stress-strain relationship becomes nonlinear.
To find the MOR, you need to find the point on the stress-strain curve where the material begins to deform plastically. This point is called the yield point.
The yield point can be difficult to identify, but there are a few methods that can be used. One method is to use the offset yield method. This method involves plotting the stress-strain curve and then drawing a line parallel to the elastic portion of the curve that is offset by a certain amount. The yield point is the point where the stress-strain curve intersects this line.
Another method for finding the yield point is to use the strain-hardening exponent. The strain-hardening exponent is a material property that is typically provided by the manufacturer. It is a measure of how much the material deforms plastically before it fails.
The MOR is the stress at which the material fails. It can be found by extrapolating the stress-strain curve to the point where it intersects the x-axis.
- Badges
- Science topic
- Similar topics
- Papers