# Obtaining yield stress knowing only Poisson's ratio and UTS?

• JebronLames9
In summary, JebronLames9 suggests that the yield strength of the solder may not be equal to the tensile strength of the shafts, due to the poor quality of the joint. He recommends using an assumption based on the soldering material, to calculate the yield stress.
JebronLames9
Greetings all,

I have been trying to find a method of calculating the yield stress for a material when only given;

-The dimensions of the shaft and solder (ie thickness of solder, length, cross sectional area)
-The Ultimate Tensile Strength of the solder
-Poisson's ratio of the solder
-The yield and ultimate tensile strength (UTS) of the shafts

The UTS of the solder is much smaller than that of the shafts so I assume that that is where it is failing first. I feel like not enough parameters are provided to produce a solution, due to not being provided the strain hardening index, the stress co-efficient or Young's modulus.

An assumption I have been thinking of using is that since the solder is very thin (0.07 cm) and is made of Silver, the UTS of the solder can be approximately equal to the yield strength. But that seems too simple for what I have been given to work with.

Am I missing something? Any advice is appreciated.

JebronLames9: I currently do not think tensile yield strength (Sty) can be obtained from tensile ultimate strength (Stu) and Poisson's ratio (nu). And I would say, Sty of solder is not approximately equal to Stu.

If you have typical tin-silver-copper solder (lead-free), I guess (?) the solder average properties are approximately Stu = 42 MPa, Sty = 28 MPa, and E = 35 GPa. How does this compare to the Stu value you currently have for your solder?

Above, I assumed typical soldering. Are you referring to soldering? Or instead brazing? In brazing, the joint is created at a temperature exceeding 450 C.

Are you sure your joint is subjected to tensile stress, instead of shear stress? In other words, are you sure you have only a butt joint, between the two bar ends, and not a lap joint?

Last edited:
What nvn said, plus the fact the 0.7 mm of solder between the two parts seems a very poor joint. The solder layer seems much too thick.

In a properly soldered joint, you have a thin layer of solder pulled into the joint by capillary action, and it forms an alloy with the materials that are being joined. Often soldered or brazed joints are actually stronger than the materials being joined.

## 1. How can Poisson's ratio and UTS be used to determine yield stress?

Poisson's ratio and ultimate tensile strength (UTS) can be used in combination with each other to calculate an estimation of yield stress. Yield stress is the amount of stress a material can withstand before permanent deformation occurs. It is directly related to both Poisson's ratio and UTS, as they both affect the material's ability to resist deformation under stress.

## 2. What is the formula for calculating yield stress using Poisson's ratio and UTS?

The formula for estimating yield stress using Poisson's ratio and UTS is given by: Yield Stress = UTS / (3 + 2 x Poisson's ratio). This formula assumes that the material follows the linear elastic behavior and does not take into account any plastic deformation.

## 3. Is the yield stress calculated using Poisson's ratio and UTS accurate?

The yield stress calculated using Poisson's ratio and UTS is an estimation and may not be entirely accurate. It is based on the assumption of linear elastic behavior and does not account for any plastic deformation. The actual yield stress may vary depending on factors such as material composition and testing conditions.

## 4. Can Poisson's ratio and UTS be used to determine yield stress for all materials?

No, Poisson's ratio and UTS cannot be used to determine yield stress for all materials. These properties are specific to each material and may vary significantly. Additionally, some materials may exhibit nonlinear behavior, making the estimation of yield stress using these properties less accurate.

## 5. Are there other methods for determining yield stress besides using Poisson's ratio and UTS?

Yes, there are other methods for determining yield stress, such as performing tensile tests and analyzing the stress-strain curve. These methods provide more accurate results, but may also be more time-consuming and require specialized equipment and expertise.

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