Three point flexural test

1940s flexural test machinery working on a sample of concrete
Test fixture on universal testing machine for three point flex test

The three point bending flexural test provides values for the modulus of elasticity in bending E_f, flexural stress \sigma_f, flexural strain \epsilon_f and the flexural stress-strain response of the material. The main advantage of a three point flexural test is the ease of the specimen preparation and testing. However, this method has also some disadvantages: the results of the testing method are sensitive to specimen and loading geometry and strain rate.

Testing method

The test method for conducting the test usually involves a specified test fixture on a universal testing machine. Details of the test preparation, conditioning, and conduct affect the test results. The sample is placed on two supporting pins a set distance apart and a third loading pin is lowered from above at a constant rate until sample failure.

Calculation of the flexural stress \sigma_f

\sigma_f = \frac{3 F L}{2 b d^2} for a rectangular cross section
\sigma_f = \frac{F L}{\pi R^3} for a circular cross section[1]

Calculation of the flexural strain \epsilon_f

\epsilon_f = \frac{6Dd}{L^2}

Calculation of flexural modulus E_f[2]

E_f = \frac{L^3 m}{4 b d^3}

in these formulas the following parameters are used:

curve,(P/D), (N/mm)

Fracture toughness testing

Single edge notch bending specimen (also called three point bending specimen) for fracture toughness testing.

The fracture toughness of a specimen can also be determined using a three-point flexural test. The stress intensity factor at the crack tip of a single edge notch bending specimen is[3]

\begin{align} K_{\rm I} & = \frac{4P}{B}\sqrt{\frac{\pi}{W}}\left[1.6\left(\frac{a}{W}\right)^{1/2} - 2.6\left(\frac{a}{W}\right)^{3/2} + 12.3\left(\frac{a}{W}\right)^{5/2} \right.\\ & \qquad \left.- 21.2\left(\frac{a}{W}\right)^{7/2} + 21.8\left(\frac{a}{W}\right)^{9/2} \right] \end{align}

where P is the applied load, B is the thickness of the specimen, a is the crack length, and W is the width of the specimen. In a three-point bend test, a fatigue crack is created at the tip of the notch by cyclic loading. The length of the crack is measured. The specimen is then loaded monotonically. A plot of the load versus the crack opening displacement is used to determine the load at which the crack starts growing. This load is substituted into the above formula to find the fracture toughness K_{Ic}.

The ASTM E1290-08 Standard suggests the relation

K_{\rm I}= \cfrac{6P}{BW}\,a^{1/2}\,Y

where

Y=\cfrac{1.99-a/W\,(1-a/W)(2.15-3.93a/W+2.7(a/W)^{2})}{(1+2a/W)(1-a/W)^{3/2}} \,.

The predicted values of K_{\rm I} are nearly identical for the ASTM and Bower equations for crack lengths less than 0.6W.

Standards

See also

References

  1. ↑ "Chapter 4 Mechanical Properties of Biomaterials". Biomaterials - The intersection of Biology and Material Science. New Jersey, United States: Pearson Prentice Hall Bioengineering. 2008. p. 152.
  2. ↑ "Activity 20 - Bendy Wafer". Salters Horners Advanced Physics for Edexcel AS Physics. Essex, United Kingdom: Pearson Education. 2008.
  3. ↑ Bower, A. F. (2009). Applied mechanics of solids. CRC Press.
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