Determination of Dynamic Fracture Toughness Using Strain Measurement

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1 Key Engineering Materials Vols (4) pp online at (4) Trans Tech Publications, Switzerland Online available since 4/4/15 Determination of Dynamic Fracture Toughness Using Strain Measurement J. H. Kim 1, D. H. Kim 1, S. I. Moon and J. H. Kim 1 Department of Mechanical Design Engineering, Chungnam National University, Kung-dong, Yusung-ku, Daejeon, , Korea Agency for Defense Development Yusung Post Office No. 35, Daejeon, 35-31, Korea Keywords: Dynamic fracture toughness, Strain measurement, Loading rate, Ti-6Al-4V, M 5, Al 775-T6, Al 7175-T74, Weibull analysis ABSTRACT By contrast with static fracture toughness determination, the methodology for dynamic fracture toughness characterization is not yet standardized and appropriate approaches must be devised. The accurate determination of the dynamic stress intensity factors must take into account inertial effects Most methods for dynamic fracture toughness measurement are experimentally complex. However, dynamic fracture toughness determination using strain measurement is extremely attractive in terms of experimental simplicity. In this study, dynamic fracture toughness tests using strain measurement are performed. High rate tension and charpy impact tests are carried out for titanium alloy, maraging steel and Al alloys. In the case of evaluating the dynamic fracture toughness using high rate tension and charpy impact tests, load or energy methods are used commonly. The consideration about inertial effects is essential, because load or energy methods are influenced by inertia. In contrast, if the position for optimum response of strain is provided, dynamic fracture toughness evaluation using strain near crack tip is more accurate. To obtain the position for optimum response of strain, a number of gages were attached at angles of 6. Reliability for experimental results is evaluated by Weibull analysis. The method presented in this paper is easy to implement in a laboratory and it provides accurate results compared to results from load or energy methods influenced by inertia. 1. INTRODUCTION A study of the dynamic fracture characteristics of engineering materials requires measuring quantities such as K Id or J Id which characterize the magnitude of the crack initiation force. Previous experimental investigations of dynamic fracture of opaque materials have involved optical methods of measurement including reflection photoelasticity, caustics and Moire interferometry. More All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, (ID: /1/8,1:3:56)

2 314 Advances in Fracture and Failure Prevention recently, strain gages have been used to measure fracture toughness in both static and dynamic applications. The use of strain gages for fracture studies was first suggested by Irwin. However, at the first stage, researchers were hesitant in using strain gages because of the large averaging errors produced due to the finite size of these gages. Since the crack tip strain field has steep gradients, the averaging errors can be very large if the strain gages are not small enough and properly placed. Therefore, to measure the reliable fracture toughness using strain measurement, the strain field near the crack tip is defined well enough to properly position and orient the strain gages[1,]. In this study, dynamic fracture toughness of structural materials for a propulsive engine are evaluated using strain measurement. To obtain the position for optimum response of strain, the number of gages were installed at various position. Reliability for experimental results is evaluated by Weibull analysis.. MATERIALS AND EXPERIMENTAL PROCEDURES This study is carried out with titanium alloy(ti-6al-4v), maraging steel(m5) and Al alloys(al 775-T6, Al 7175-T74) using propulsive engine materials whose mechanical properties(as measured in our laboratory) are listed in Table 1. Compact tension(ct) and three point bend(3pb) specimens are machined according to ASTM E399[3]. The specimens were all manufactured from the same plate and care was exerted to have all slits oriented in the same direction. Sharp notches were machined by wire discharge manufacturing. The test procedures were performed in accordance with ASTM E399[3]. Pre-cracking of the fracture toughness test specimen was carried out by a fatigue test machine. Pre-crack was controlled by a moveable digital microscope. Slit lengths of specimens were controlled a/w.48. Precracking and static fracture toughness test were performed using a hydraulic fatigue test machine (Shimadzu, model EHF-ED1). The static specimens were loaded at a loading speed of.5mm/min. The dynamic fracture toughness tests are performed using instrumented charpy impact and high rate tension testers. The impact velocity is controlled by 5.15m/s in order to compare the specimen types. The strain gage attachment position to evaluate the fracture toughness will be demonstrated in the next chapter. Strain was measured by strain conditioner amplifier (Measurement group, Model : 1). Signals from the strain amplifier are converted by A/D board. The data acquisition system is programmed by LabView. Table 1. Mechanical properties of test materials Properties M5 Ti-6Al-4V Al 775-T6 Al 7175-T74 Young s modulus (GPa).% Yield strength (MPa) Tensile strength (MPa) ,56 1, ,6 1, Poisson s ratio, Elongation (%)

3 Key Engineering Materials Vols EVALUATION OF FRACTURE TOUGHNESS USING STRAIN MEASUREMENT The Westergaard equations are used in the solution of fracture mechanics problems. These equations with parameters including the location of free surfaces and the point of application of forces were generalized by Sanford. The strain field of Westergaard equations is given as[1,], ' ' E xx ( 1) Re Z (1 + ) y Im Z (1 + ) y Im Y + ReY (1) where, Poisson s ratio, EYoung s modulus and prime denotes a first derivative with respect to z x + iy. For one edge crack problem, eqn. (1) can be solved with the help of the stress function. Z( z) N n A n z n1/ N Y ( z ) n B z m m () If n, 1 and m, 1, the strain expressions can be obtained as follows, E 1/ xx Ar cos( / )[(1 ) (1 + )sin( / ) sin(3 / )] 1 / + B + A r cos( / )[(1 ) + (1 + ) sin ( / )] 1 + B 1 r cos (3) The number of strain gages are reduced using the strains relative to a rotated coordinate system (x,y) with its origin at an arbitrary point P(r,) as defined in Fig. 1. Substituting eqn. (3) into the complex form of the strain-transformation equations leads to, 1/ µ Ar [ k cos( / ) (1/ ) sin sin(3 / ) cos + ( 1/ ) sin cos(3 / ) sin ] + B ( k + cos ) + A 1 / 1r cos( / )[ k + sin ( / ) cos (1/ ) sin sin ] + B1r[( k + cos )cos sin sin ] (4) where, k ( 1 ) /(1 + ) The orientation of the gage is obtained by simplifying eqn. (4). A careful examination can reveal that the parameters B and A 1 are eliminated by equating their coefficients to zero as, cos k (1 ) /(1 + ) (5) and, k + sin ( / ) cos (1/ )sin sin (6) Therefore, for the aluminum alloys to be tested, the strain gage is placed at 6.5, 6.1. The stress intensity factor is determined using eqn. (4) as follows Fig. 1 Definition of coordinate system O xy and P x y

4 316 Advances in Fracture and Failure Prevention K And, K I I.914E r.95731e r (.33 : Al alloys) (7) (.31 : Maraging steel, Titanium alloy, 6.89, ) (8) 4. RESULTS AND DISCUSSION Fig. shows the strike force and strain versus time response of 3PB specimen by charpy impact tester. Fig. 3 shows the dynamic test results of load, displacement and strain versus time for CT specimen using high rate tension tester. As you can see the Fig., the maximum force rises before the maximum strain for charpy impact test. In the case of using high rate tension tester, time to the maximum strain increases early. For maraging steel tested by charpy impact tester, we can easily determine the crack initiation load because inertia force and dynamic crack initiation load appeared to be separated distinctly with full capacity. Table presents the average values for the static and dynamic fracture toughness. To exclude the inertia effects, compensated K Id is calculated in which original load signals subtract the acceleration signals. K Id-Load is calculated by a linear dynamic fracture mechanics equation[4]. This equation is available where the load is seen to increase linearly until maximum load is reached where fracture is initiated. K Id-Energy is calculated by Ronald s energy equation[5]. Striker force(n) Striker force Strain Time(µs) (a) M Strain (µ) (b) Ti-6Al-4V Fig. Strike force and strain versus time response of 3PB specimen Striker force(n) Striker force Strain Time(µs) Strain (µ µ) Load (N), Strain (x1 µ) compensated load original load strain Ch#1 strain Ch# displacement Time ( µs ) Displacement (m) Load (N), Strain (1 x µ) load strain ch#1 strain ch# displacement Time(µs) Displacement (m) (a) M5 (b) Ti-6Al-4V Fig. 3 Test recording of load, displacement and strain versus time of CT specimen

5 Key Engineering Materials Vols Table Average values of static and dynamic fracture toughness for maraging steel and titanium alloy Materials M5 Ti-6Al-4V 3PB specimen CT specimen 3PB specimen CT specimen Static K IC-Strain (MPa m ) K IC-ASTM K Id-Strain K Id-ASTM Dynamic Compensated (MPa m ) K Id-ASTM K Id-Load K Id-Energy Failure probability (%) Failure probability (%) Dynamic fracture toughness (MPa m 1/ ) Dynamic fracture toughness (MPa m 1/ ) (a) Al 775-T6 (b) Al 7175-T74 Fig. 4 Weibull distribution of dynamic fracture toughness 4 4 K I-Strain & K I-ASTM ( MPa m 1/ ) 3 1 CT : Al775-T6(static:strain) CT : Al775-T6(static:ASTM) CT : Al775-T6(dynamicc:strain) CT : Al775-T6(dynamic:ASTM) r/w K I-Strain & K I-ASTM ( MPa m 1/ ) 3 1 CT : Al7175-T74(static:strain) CT : Al7175-T74(static:ASTM) CT : Al7175-T74(dynamicc:strain) CT : Al7175-T74(dynamic:ASTM) (a) Al 775-T6 (b) Al 7175-T74 Fig. 5 Influences of r/w for static and dynamic fracture toughness results for Al alloys r/w Venkatanarayana[6] reported that the strength properties of M5 are independent of strain rate. In contrast, there is a considerable difference between the K IC and K Id values for the Ti-6Al-4V; namely, K IC increases by more than 47% with increasing loading rates. A similar positive loading-

6 318 Advances in Fracture and Failure Prevention rate sensitivity of fracture toughness was observed for another titanium alloy[7]. As pointed out by Klepaczko[8], this behavior may be attributed to a direct decrease in flow stress due to adiabatic heating at the crack tip under high strain rates because of the low thermal conductivity of the titanium alloy. Therefore, experimental data of CT specimen obtained from strain measurement coincides well with reference results[6-8]. The dispersion characteristics of K Id for Al alloys evidently conform to the Weibull distribution (Fig. 4), which is expressed as follow: F K 1 exp IC where, is the shape parameter and is the scale parameter. While the loading rates for the static and dynamic tests differ by six orders of magnitude, the fracture toughness for the Al alloys remain nearly unchanged(al 775-T6 : K IC, K Id 5-7 ; Al 7175-T74 : K IC, K Id 4-5 MPa m ). This is because the Al alloy exhibits essentially no strain rate sensitivity up to a strain rate of about 6s -1. Fig. 5 shows the influences of r/w for static and dynamic fracture toughness results for Al alloys. Where, r means the distance from crack tip to strain gage position and W is specimen width. Static fracture toughness by ASTM agrees with the results obtained from strain measurement above r/w.8. For dynamic fracture toughness, strain measurement results coincide with ASTM results above r/w.75. (9) 5. CONCLUSIONS (1) Strain measurement technique can simply determine the dynamic fracture toughness. () Fracture toughness of maraging steel(k IC, K Id MPa m ) and Al alloys(al 775-T6 : K IC, K Id 5-7 ;. Al 7175-T74 : K IC, K Id 4-5 MPa m ) are independent of loading rate. For titanium alloys, dynamic fracture toughness increases as the loading rate increases(k IC 4-45MPa m, K Id 6-63MPa m ). (3) For Al 775-T6 and Al 7175-T74, the static and dynamic fracture toughness obtained from strain measurement coincide with results by ASTM above r/w.8. REFERENCES 1. J. W. Dally and R. J. Sanford, Exp. Mech., 7 (1987) p.381. L. Parnas and O. G. Bilir, Eng. Fract. Mech., 55 (1996) p ASTM E399, Metals Test Methods and Analytical Procedures, 3 (1997) p T. J. Koppenaal, Instrumented Impact Testing, ASTM STP 563 (1974) p.9 5. A. Ewing and L. Raymond, Instrumented Impact Testing, ASTM STP 563 (1974) p G.. Venkatanarayana, S. Arumugham, T. S. Lakshmanan and P. P. Rao, Mat. Sci. Technol., 1 (1996) p T. Yokoyama and K. Kishida, Exp. Mech., 9 (1989) p J. R. Klepaczko, Theor. Appl. Fract. Mech., 1 (1984) p.181