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.
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 defined as
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).
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 1.
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 / sy)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.
Figure 1. Schematic of the typical load-COD plot obtained in a fracture toughness experiment.
W.T. Matthews, Plane Strain Fractue Toughness (KIc) Data Handbook for Metals, AMMRC MS73-6, U.S. Army Materials and Mechanics Research Center, Watertown, MA, 1973.
Damage Tolerant Design handbook, Metals and Ceramics Information Center, Battele Columbus Laboratories, Columbus, Ohio, 1975.
C.M. Hudson and S.K. Seward, "Compendium of Sources of Fracture Toughness and Fatigue Crack Growth Data for Metallic Alloys," International journal of Fracture, V. 14, 1978, pp. R151-R184.
C. Hudson, S.K. Seward, "A Compendium of Sources of Fracture Toughness and Fatigue Crack Growth Data for Metallic Materials, Part II," Int. J. Frac., V. 20, 1982, pp. R59-R117.
|B =||mm||Pmax =||N|
|a =||mm||Pmax/PQ < 1.10 ?|
|PQ =||N||B, a, (w-a) > (KQ / sy)2 ?|
|sy=||MPa||Invalid Test ?|
|KQ=||MPa||Valid Test KIC = KQ =||MPa|
|(KQ / sy)2||mm|
Representative data for KIc for several metals
are given in Table 1, along with the values of corresponding critical
plastic zone sizes. Also include in Table I is the crack length
L* = 2a° which in a Griffith crack configuration would cause
fracture initiation at an applied stress of (1/2)sy.
Note that L* is essentially the characteristic length dimension
which specimen crack length, remaining ligament and thickness
must exceed in order to obtain a valid KIc value
for material. The combination of high KIc
and low sy leads to relatively large
values of critical plastic zone size, and rather long cracks are
required before initiation will occur at stress levels which are
some fraction of the general yield stress.
|Medium carbon (AISI-1045)|
|Pressure Vessel (ASTM-A5330-B)|
|High Strength Alloy (AISI-4340)|
|Maraging Steel (250-Grade)|
|WC - 15 wt% Co (cermet)|