TensileTest¶

class mechanical_testing.TensileTest(file, length, diameter)¶

Process tensile testing data.

Load a tensile test data and process it in order to deliver the material properties.

Warning

All values are meant to be in the SI units. Since no unit conversion is made, the input data has to be in the SI units.

originalFile¶

Path to the file from which the data was read.

Type: str

force¶

Force data from the tensile test.

Type: numpy.ndarray

displacement¶

Displacement data from the tensile test.

Type: numpy.ndarray

time¶

Time instant data from the tensile test.

Type: numpy.ndarray

length¶

Gage length of the specimen.

Type: float

diameter¶

Diameter of the specimen.

Type: float

area¶

Cross section area of the specimen. \(A = \dfrac{\pi \ D}{4}\) being \(D\) the diameter of the specimen.

Type: float

strain¶

Strain data of the tensile test. \(\epsilon = \dfrac{l - l_0}{l_0} = \dfrac{d}{l_0}\) being \(l_0\) the initial length.

Type: numpy.ndarray

stress¶

Stress data of the tensile test. \(\sigma = \dfrac{F}{A}\) being \(F\) the force and \(A\) the cross section area.

Type: numpy.ndarray

realStrain¶

Strain for the real curve. \(\epsilon_r = ln(1 + \epsilon)\).

Type: numpy.ndarray

realStress¶

Stress for the real curve. \(\sigma_r = \sigma \ (1 + \epsilon)\).

Type: numpy.ndarray

proportionalityStrain, proportionalityStrength

Stress and strain values at the proportionality limit point.

Type: float

yieldStrain, yieldStrength

Stress and strain values at the yield point.

Type: float

ultimateStrain, ultimateStrength

Stress and strain values at the ultimate point.

Type: float

strengthCoefficient, strainHardeningExponent

Those are coefficients for the Hollomon’s equation during the plastic deformation. It represents the hardening behavior of the material. Hollomon’s equation: \(\sigma = K \ \epsilon^{n}\) being \(K\) the strength coefficient and \(n\) the strain hardening exponent.

Type: float

elasticStrain, elasticStress

Strain and stress data when the material behaves elastically.

Type: numpy.ndarray

plasticStrain, plasticStress

Strain and stress data when the material behaves plastically.

Type: numpy.ndarray

neckingStrain, neckingStress

Strain and stress data when the necking starts at the material.

Type: numpy.ndarray

elasticModulus¶

Elastic modulus value.

Type: float

resilienceModulus¶

Resilience modulus value. It is the energy which the material absorbs per unit of volume during its elastic deformation.

Type: float

toughnessModulus¶

Resilience modulus value. It is the energy which the material absorbs per unit of volume until its failure.

Type: float

See also

Tensile testing wikipedia page

Stress-Strain curve wikipedia page

Notes

Title¶
Symbol	Description	Definition
\([F]\)	force	input
\([d]\)	displacement	input
\([t]\)	time	input
\(l_0\)	specimen length	input
\(D\)	specimen diameter	input
\(A\)	specimen cross section area	\(A = \dfrac{\pi \ D^2}{4}\)
\([\epsilon]\)	strain	\(\epsilon = \dfrac{l - l_0}{l_0} = \dfrac{d}{l_0}\)
\([\sigma]\)	stress	\(\sigma = \dfrac{F}{A}\)
\([\epsilon_r]\)	real strain	\(\epsilon_r = ln(1 + \epsilon)\)
\([\sigma_r]\)	real stress	\(\sigma_r = \sigma \ (1 + \epsilon)\)
\(\epsilon_{pr},\sigma_{pr}\)	proportionality strain and strength	algorithm defined
\(\epsilon_y,\sigma_y\)	yield strain and strength	algorithm defined
\(\epsilon_u,\sigma_u\)	ultimate strain and strength	algorithm defined
\(K\)	strength coefficient	algorithm defined
\(n\)	strain hardening exponent	algorithm defined
\([\epsilon_e]\)	elastic strain	\([\epsilon][\epsilon < \epsilon_y]\)
\([\sigma_e]\)	elastic stress	\([\sigma][\epsilon < \epsilon_y]\)
\([\epsilon_p]\)	plastic strain	\([\epsilon][\epsilon_y < \epsilon < \epsilon_u]\)
\([\sigma_p]\)	plastic stress	\([\sigma][\epsilon_y < \epsilon < \epsilon_u]\)
\([\epsilon_n]\)	necking strain	\([\epsilon][\epsilon_u < \epsilon]\)
\([\sigma_n]\)	necking stress	\([\sigma][\epsilon_u < \epsilon]\)
\(E\)	elastic modulus	\(\sigma = E \ \epsilon\), curve fit
\(U_r\)	resilience modulus	\(\displaystyle\int\limits_{[\epsilon_e]}\sigma \ \mathrm{d}\epsilon\)
\(U_t\)	toughness modulus	\(\displaystyle\int\limits_{[\epsilon]}\sigma \ \mathrm{d}\epsilon\)

Auto-find proportionality limit and elastic modulus:

foreach l in range(10, len(strain)):
        fit a one-degree polynomial to the data
        store the linear coefficient
        store the curve fit residual
select the proportionality limit point as the one with the smallest residual
select the elastic modulus as the linear coefficient of the polynomial

Ultimate point:

Select the ultimate point as the one
with the maximum stress

Yield point:

select the yield point as the intersection of the curves:
        ([strain], [stress])
        ([strain], elasticModulus * ([strain]-0.002))
if the point has strain larger than the ultimate point:
        select the yield point as equals to the
        proportionality limit point

Hardening, strength coefficient and strain hardening exponent:

Curve fit (Hollomon's equation):
        f = K * strain**n
        x = [plastic strain]
        y = [plastic stress]

__init__(file, length, diameter)¶

Process tensile data.

Parameters

file (str) – Path to file containing the data. The data from the file is not checked in any way. The file must be in the comma-separated-value format.
length (float) – Length \(l_0\) of the specimen in meters.
diameter (float) – Diameter \(D\) of the specimen in meters.

Examples

>>> import mechanical_testing as mect
>>> tensile = mect.TensileTest(
                file     = './test/data/tensile/tensile_steel_1045.csv,
                length   = 75.00E-3,
                diameter = 10.00E-3,
)
>>> tensile.yieldStrength
7.6522E+8

offsetYieldPoint(offset)¶

Yield point defined by the input offset

Parameters: offset (float) – Offset value. For the common yield point used in engineering, use offset = 0.002 = 0.2%.
Returns: (strain, stress) ((float, float)) – Yield point equivalent to the input offset.