Fracture Mechanics

By: kalyan kumar dhar

Objectives

1. To make a valid measurement of the plane strain fracture toughness of a given material.

2. To observe and understand a typical brittle fracture process.

Background

Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials? is most often tested according to ASTM E 399? specifications. The KIC test or KIC, or K1C, as it is also known, is used to determine the fracture toughness of metallic materials.

?The phenomenon of brittle fracture deals with sudden failure of structural components without warning. This is attributed to presence of cracks or crack-like defects in the material that appear during processing or during fabrication and assembly of the component. The theory behind this phenomenon, as it applies to many engineering structures, is referred to as Linear Elastic Fracture Mechanics (or LEFM). According to this theory, the condition for brittle failure can be expressed as

where KI is called the stress intensity factor and is dependent on loading conditions and the flaw size in the material, and KIC is a material property known as the plane strain fracture toughness. The stress intensity factor is usually expressed as

where Q is a geometry correction factor depending on the geometry of the structural component and the crack geometry, ?is the applied stress, and 'a' denotes the crack size. Definitions of these quantities for many typical situations are presented in an Appendix at the end of this handout for your convienience. Finally note that KI and KIC have dimensions of stress (i.e. Mpa or ksi ).

In order to use the above criterion for fracture two conditions have to be met. These are

(i) small scale yielding condition. All in-plane dimensions of the component as well as the crack size should be larger than fifteen times the critical plastic zone size (rIC), which is a

where ?is the yield strength of the material.

(ii) plane strain condition. The thickness of the sample should also be larger than fifteen times the critical plastic zone size (rIC).

Experimental Procedure

The ASTM standard (E399) for plane strain fracture toughness testing provides a procedure for calculating values of KIC for metallic materials. The test permits three different specimen shapes: a bend specimen, a C-shaped specimen, and a compact test specimen (CTS). The CTS will be used in this laboratory.

The procedure for measuring KIC with a CTS is as follows:

1. Make a guess of the expected value of KIC. This enables you to calculate an estimated critical plastic zone size.

2. To ensure that only small-scale yielding occurs at the crack tip, the length, a, of the crack and the remaining ligament, (W - a), should be greater than or equal to 15rIC.

a, (W - a ) " 15rIC.

3. To ensure plane strain, the thickness, B, of the CTS should be greater than or equal to 15rIC.

B " 15rIC.

4. Once a CTS is machined, according to the dimensions calculated above, a sharp crack is introduced at the root of the machined notch. This is accomplished by fatigue pre-cracking the specimen. This procedures involves imposing a time-varying tensile load on the CTS to cause a sharp crack to initiate and slowly grow at the root of the machined notch. The maximum fatigue load should be less than 0.6 times the value of the estimated final fracture load:

Pfmax " 0.6 PQ.

5. The fatigue-generated protion of the crack should be at least 1.2 mm long.

6. Once a sharp crack exists, the actual KIC test can be performed. The test consists of increasing the tensile load, P, on the specimen slowly while measuring the crack opening displacement, Æ. Plotting the P versus Æ produces a curve similar to the one shown in Figure 1. Fast fracture is indicated by a gross nonlinearity in the load-displacement record.

7. To calculate the KIc, first calculate a conditional KQ using

?The geometric variables a, W, and B are defined in the sample schematic in the datasheet. Determine, a, by measuring the initial crack length (notch plus fatigue pre-crack). PQ is determined by projecting a line whose slope is five percent less than the original slope of the P - Æ curve. PQ is the load corresponding to the intersection of this line with the P - Æ curve. See Figure 2.

Figure 2. Schematic of the typical load-COD plot obtained in a fracture toughness experiment.

8. The ratio Pmax/PQ should be less than 1.10, where Pmax is the maximum load encountered in the test.

Pmax / PQ < 1.10.

9. If condition 8 holds, then calculate ?(KQ / s sn)2 . If this quantity is less than the specimen thickness, B, the crack length, a, and the remaining ligament (W - a), then KQ is equal to KIc. Otherwise the test is not a valid KIc test.

Results and Verification:

Requirement for verification :

0,45?a/W?0,55?

?????????????????????????? B,(W-a)?2,5(KQ/?s sn)2?????????????????????? ????? ????? ??????

?????????????????????????? Pmax?1,10PQ

If above three conditions are verified, as a consequnce:

???????????????????? KQ=Kic

From our experiment,? We can get following data:

PQ=Pmax=6100N

?

f(a/W)=f(0.5)=10.1375

?

KQ=26.1 MPa m^0.5

?

Bmin=2.5x(KQ/Rs)=2.5x(26.1/1080)^2=0.0014 m

???

?The toughness is influenced by the thickness. The stress intensity factor has not a physical meaning. The cracked structure fails because the stress field near the crack tip becomes critical values.?? .

?

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