A.K. Ray, E.R. Fuller, S. Banerjee 3.3 Determination of fatigue crack growth rate monotonic loading; the ramp rate was 0.25 N s FCGR The load value corresponding to the onset of fast FCGR was determined after the crack had grown fracture was used in eqn (1)to obtain the K ignificantly on the side surfaces during precrack value. Since four- point bend specimens were used 0.05 to 0. 1. The four-point bend specimen is not to the mcthod givcn clscwhcrc 6/S in all respects ing and achieved length a equivalent to a/w Kic testing followed here conforme recommended in Astm Standard E647 and In addition to this procedure, the indentation therefore, the k values of the specimen were cal- fracture toughness Kc of this material was deter culated using the standard formula reported else- mined from the indentation technique at various (referred to as the ASTM STP 410 loads(0 63, 0-8, 1-0 and 1.2 kN using the follow method). Except for this aspect and the use of an ing equation proposed by anstis et al. 8 indentation as a crack starter, the procedure used here to determine fcgr conformed to the recom- K=0061E.P h a mendations given in ASTM Standard E647 The tests were conducted in an MTS-880 servo- where E is the Young's modulus, H is the hardness, hydraulic test machine using a I kN load cell P is the load and a the crack length. Many emper- under four-point bend loading, in laboratory cal expressions to evaluate indentation fracture atmosphere and at ambient temperature. The toughness have been reported in the literature. 19 loading rate was 0.25 s. The frequency wa However, in the case of toughened Hz and r= 01. Typically, the specimens were adial cracks are emanating at the four corners of cycled within the load range between 11 and 11 the Vickers indentation, 9 the above model [eqn(2)1 N, when a/w=0-1. The crack lengths were mes has been used by Anstis et al. to determine Ko sured at regular increments of number of cycles giving 0-05 to 0.1 mm of crack growth. While 3.5 SEM studies measuring the crack length, the specimen was first The fracture surfaces of the test specimens were unloaded from the servohydraulic machine and coated with a thin film of gold (thickness 0-02 um) the current crack length was measured with the and then examined g the scanning electron help of the micron marker in the SEM. Thus the microscope to identify the characteristic fracto fatigue cracking was interrupted after a predeter- graphic features of the fatigue and fast fracture mined number of load cycles. This was continued regions in this material. The identification of these until the crack length increased to a value giving features gives a clue as to the likely mechanisms of a/W-045to0.5 fracture for this material The test data of crack length were plotted in At first, the SEM examination of the fatigue tcrms of crack length a vS. numbcr of cycles N. fracture and fast fracture zones was carried out at The values of da/dN were generated from the a vs low magnification of 30X. Thereafter, each of N plot at any given a and plotted against AK these zones was scanned at 4500x and 7500x (stress intensity range). With load and a known, The fatigue crack growth at the low AK region K values were calculated from and the fast fracture region(due to monotonic K - Y3P(L L,)v/2bw () tify and distinguish between the characteristic where fractographic features Y=199-247(a/W)+1297(a/W) 2317(a/W)3+2480(a/W 4 Results P=load; L, external span; L2 internal span b= thickness of specimen;W= depth or width 4.1 Fracture toughness data of specimen; a= crack length. The values of Kmax Fracture toughness values determined in this pro and Kmin were calculated using eqn(1). The AK ject, using both the indentation technique as well value is given by kmax -kmi as the ASTM STP 410 method with precracked specimens, are reported in Table 1. Indentation 3.4 Fracture toughness(Kic) testing fracture toughness test data determincd with a After the FCGr determination was complete and Vickers indentation at various loads of 0-63,0-80, he crack had grown to a level of a/w =0-45 1- 0 and 1. 2 kN yielded Kc values of 537, 5 45, 5.5 0.5, Kc was determined by subjecting the pre- and 5 6 MPa m", respectively. Figure 3 shows the variation of indentation fracture to oughness values loading. The test record of load vs. mid-point dis- with the square root of the corresponding crack placement of the specimen was obtained during lengths. It was observed (see Fig. 3)that the506 A. K. Ray, E. R. Fuller, S. Banerjee 3.3 Determination of fatigue crack growth rate (FCGR) FCGR was determined after the crack had grown significantly on the side surfaces during precrack￾ing and achieved length a equivalent to a/W = 0.05 to 0.1. The four-point bend specimen is not recommended in ASTM Standard E647 and, therefore, the K, values of the specimen were cal￾culated using the standard formula reported else￾where’6,‘7 (referred to as the ASTM STP 410 method). Except for this aspect and the use of an indentation as a crack starter, the procedure used here to determine FCGR conformed to the recom￾mendations given in ASTM Standard E647. The tests were conducted in an MTS-880 servo￾hydraulic test machine using a 1 kN load cell under four-point bend loading, in laboratory atmosphere and at ambient temperature. The loading rate was 0.25 N s?. The frequency was 1 Hz and R = 0.1. Typically, the specimens were cycled within the load range between 11 and 111 N, when a/W = 0.1. The crack lengths were mea￾sured at regular increments of number of cycles giving - 0.05 to 0.1 mm of crack growth. While measuring the crack length, the specimen was first unloaded from the servohydraulic machine and the current crack length was measured with the help of the micron marker in the SEM. Thus the fatigue cracking was interrupted after a predeter￾mined number of load cycles. This was continued until the crack length increased to a value giving a/W = 0.45 to 0.5. The test data of crack length were plotted in terms of crack length a vs. number of cycles N. The values of da/dN were generated from the a vs. N plot at any given a and plotted against AK (stress intensity range). With load and a known, KI values were calculated from16,‘7 KI= Y3P(L,-L,)da/2bW2 (1) where Y = 1.99 - 2.47 (a/W) + 12.97 (a/v2 - 23.17 (alW’j3 + 24.80 (a/w4 P = load; L1 = external span; L, = internal span; b = thickness of specimen; W = depth or width of specimen; a = crack length. The values of Km,, and Kmin were calculated using eqn (I). The AK value is given by Km,, - Kmi,. 3.4 Fracture toughness (K,,) testing After the FCGR determination was complete and the crack had grown to a level of a/W = 0.45 to 0.5, K,, was determined by subjecting the pre￾cracked four-point bend specimens to monotonic loading. The test record of load vs. mid-point dis￾placement of the specimen was obtained during monotonic loading; the ramp rate was 0.25 N ss’. The load value corresponding to the onset of fast fracture was used in eqn (1) to obtain the K,, value. Since four-point bend specimens were used, K,, testing followed here conformed in all respects to the method given elsewhere.‘6,‘7 In addition to this procedure, the indentation fracture toughness Kc of this material was deter￾mined from the indentation technique at various loads (0.63, 0.8, 1 .O and 1.2 kN) using the follow￾ing equation proposed by Anstis et al.‘* Kc = 0.016 1/ $. -$ where E is the Young’s modulus, H is the hardness, P is the load and a the crack length. Many emper￾ical expressions to evaluate indentation fracture toughness have been reported in the literature.]’ However, in the case of toughened ceramics where radial cracks are emanating at the four corners of the Vickers indentation,” the above model [eqn (2)] has been used by Anstis et al.‘* to determine Kc. 3.5 SEM studies The fracture surfaces of the test specimens were coated with a thin film of gold (thickness 0.02 pm) and then examined using the scanning electron microscope to identify the characteristic fracto￾graphic features of the fatigue and fast fracture regions in this material. The identification of these features gives a clue as to the likely mechanisms of fracture for this material. At first, the SEM examination of the fatigue fracture and fast fracture zones was carried out at a low magnification of 30X. Thereafter, each of these zones was scanned at 4500X and 7500X. The fatigue crack growth at the low AK region and the fast fracture region (due to monotonic loading) were carefully examined in order to iden￾tify and distinguish between the characteristic fractographic features. 4 Results 4.1 Fracture toughness data Fracture toughness values determined in this pro￾ject, using both the indentation technique as well as the ASTM STP 410 method with precracked specimens, are reported in Table 1. Indentation fracture toughness test data determined with a Vickers indentation at various loads of 0.63, 0.80, 1.0 and 1.2 kN yielded Kc values of 5.37, 5.45, 5.5 and 5.6 MPa m1’2, respectively. Figure 3 shows the variation of indentation fracture toughness values with the square root of the corresponding crack lengths. It was observed (see Fig. 3) that the