Study on the behavior of foam material with high ...

Asian Symposium for Precision Engineering and Nanotechnology 2009

Study on the behavior of foam material with high strain rate fatigue Jae Ung Cho1,#, Liyang Xie2, Chongdu Cho3 and Sang-kyo Lee3 1 Div. of Mechanical & Automotive Engineering, Kongju Univ., 275 Budae-Dong, Seobuk-Gu, Cheonan, KOREA 2 the Institute of Modern Design and Analysis, P. O. Box 319, Northeastern University, Shenyang, 110004, P. R. CHINA 3 Department of Mechanical Engineering, Inha Univ.,253 Yonghyun-Dong, Nam-Gu, Incheon, KOREA # Corresponding Author / E-mail: [email protected], TEL: +82-41-521-9271, FAX: +82-41-555-9123 KEYWORDS : foam material, high strain rate, fatigue life, centre cracked tension (CCT) specimen, crack growth rate, stress intensity factor

Failure of foam materials under single and repeated impacts is of great concern to designers and researchers to implement its applications in military and aerospace structures. The material failure which is induced by a repeated impact loading is major concern because there is a significant loss of stiffness and compressive strength of the foam material. Testing methods used for studying the impact fatigue are quite diverse. Hence, there is no standard testing procedure for studying the high strain rate (impact) fatigue property for any kind of material. With the increasing application of foam material in aerospace structures, owing to its high specific stiffness and strength, there is a great concern toward the high sensitivity for impact damage, imparted during the manufacture or in service, and its subsequent effect on material degradation. The objective of this study is to investigate the effect of low or high strain rate on the fatigue properties of nickel foam material and to understand the lifetime of this material subjected to repeated impacts at different energy levels. This study is based on experimental and numerical investigations on the impact fatigue behavior of nickel foam with an open type. The experiments are carried with rod up and down at the high strain rate fatigue of loading cycle rate with 1 cycle/s. The experimental specimen size is 320×70×5 mm. Stress and strain at the crack initiation are measured experimentally by a strain gauge attached on the specimen surface and these values are compared with numerical values obtained through numerical simulations. Design life and probability of failure or reliability are estimated. Fatigue life of nickel core material subjected to repeated impact loading is predicted. Experimental results are compared with the numerical solutions by following FEM approach. Manuscript received: July 15, 2009 / Accepted: August 15, 2009

NOMENCLATURE 2a = center crack length w = width of specimen N = number of cycles C, m = material properties K = stress intensity factor Y= Isida’s geometrical constant

1. Introduction Metallic foams are used in wide range of applications such as delicate electronic component packaging, cores of light-weight structural sandwich panels, and in the field of sound and energy absorption. Improving structural efficiency requirement at relatively low cost has generated significant interest among cellular materials recently. It is the metallic material easy to fabricate. The properties of foams can be made to vary significantly with depending on the choice of cell-wall material and the volume fraction of the solid and the geometry of the structure. Sugimura et al. [1] and Grenestedt [2] assessed the role of cell morphology and related imperfections in governing the basic properties such as stiffness, yield strength and fracture resistance[3-5]. In view of emerging applications, detailed

characterization of mechanical behavior of metal foam is an important task in order to assess their performance. In some foam applications, it may become necessary to introduce holes or notches for fastening. These can cause a severe drop in load bearing capability of the component. An understanding of the behavior of foams in the presence of notches will be helpful in design improvement. The objective of this study is to develop such an understanding. In particular, our objective is to examine if the notch sensitivity characteristics of metallic foams [6] are similar to those of fully dense metals. In this work, an experimental investigation is carried out on open cell nickel foam and the preliminary experimental observations are presented here. This paper aims toward an experimental and numerical simulation of the behavior of fatigue crack traveling between holes or particles. Even though the experimental values are obtained from the digital camera attached to experimental setup, it is believed to able to capture the fundamental changes, such as crack propagation in a material under tension load. In addition, the result for three different specimen geometries introduced in the foam is compared for their effect on stress intensities. Finally, the response of the nickel foam on the basis of crack length is performed. Results obtained from this work can be used in practical applications involving a foam material. Distribution of cracks inside the material can affect the overall fracture rate of a material and its functioning. Substitution of another material or


material defects may lead to crack initiation and propagation [7-10]. Hence it is necessary to investigate a material for its response under various geometrical changes in order to understand the crack propagation as well as the crack arrest phenomenon. Crack propagation and stress intensity factor variation along a crack length are initially investigated under no-hole, 2-hole, and 4-hole conditions. Stress intensity factor variation under fatigue cycles is also investigated.

2. Specimens and experimental procedure Fig. 1 shows the nickel foam specimen of open-cell type for the tensile test. Tensile Stress-strain response and corresponding material properties of the specimen are shown in Fig. 2 and Table 1 respectively.

Fig. 3 Experimental set up

Fig. 1 Tensile test specimen (thickness: 5mm)

Fig. 4 Fatigue test specimen (centre cracked tension (CCT) specimen without hole)

Fig. 5 Fatigue test specimen (centre cracked tension (CCT) specimen with 2 holes)

Fig. 2 Stress-strain response Table 1. Physical data of material Modulus of elasticity (MPa)

177

Poisson’s ratio

0.30

Fatigue tests were performed by hydraulic universal test machine (landmark 100 ton, MTS Co.) as shown in Fig. 3. The geometrical parameters for the basic fatigue test specimen (320 mm gauge length, 70 mm width, and 5 mm thickness) are shown in Fig. 4. Centre hole was machined to high precision by drilling. In fact, this hole is very small in diameter (3 mm) and is not regard as a geometrical defect. As seen from Fig. 4, a small notch (slit) is made on upper and lower vicinity of the hole to imitate a crack and it is about 0.35 mm each. Fig. 5 or Fig. 6 shows the central hole with end-notches surrounded by two or four holes of 4 mm diameter respectively. The applied loading conditions are shown in Table 2. Loading was displacement control. For investigating the rate dependent characteristics of the specimen, displacement amplitude of 1.5 mm per one second is applied. It means that the strain rate was 0.015 per second for an effective total specimen length of 100 mm (excluding gripping length). The crack length was determined at regular intervals by digital camera.

Fig. 6 Fatigue test specimen (centre cracked tension (CCT) specimen with 4 holes) Table 2. Conditions of fatigue test for CCT specimens Mean displacement

1 mm

Displacement amplitude

0.5 mm

Cycle rate

1 Hz

3. Numerical analysis 3.1 Finite element model Fig. 7 shows the finite elemnt models used for our study. For obtaining the precise results,crack tips were fine meshed. The 4-node bilinear plane stress quadrilateral (CPS4R) elements were used and a linear static analysis is performed on specific crack size in combination with measured experimental results.


4.2.1 Result of CCT specimen without any hole Experimental and numerical simulation of fatigue failure in CCT specimen without hole (Fig. 4) is presented in Fig. 10. Fatigue crack propagates from pre-crack tip in the center. Crack length along load cycles can be measured by an attached paper scale.

Fig. 10 Fatigue fracture in specimen without hole (left) and FEM stress analysis (right) results of fatigue fracture without hole

Fig. 7 Finite element modeling

3.2 Crack seam The length of crack can be simply defined as a crack seam in ABAQUS/Standard. In the finite element analysis, measured crack lengths at the specific time intervals is made equivalent to specific number of cycles. Crack seam is defined as in Fig. 8.

The stress intensity factor at a specific crack length is calculated from stress analysis result and is compared with Isida’s stress intensity factor solution (1) about CCT [11].

K = s aY (1)

Y = 1.77[1 - 0.1(2a / W ) + (2a / W ) 2 ] Both of calculated stress intensity factors from FEM and Isida’s are compared and observed to be almost similar as shown in Fig. 11. However, for over 5,500 cycles, there is some difference. This is attributed to the compressive hardening which has occurred at an edge of the specimen when the specimen was manufactured.

Fig. 8 Defining crack seam

4. Result and discussion 4.1 Crack length measurement

Fig. 11 Experimental and FEM results of variation of stress intensity factor for number of loading cycles

Fig. 9 Crack growth curves for nickel CCT specimen Crack lengths for CCT specimens are shown in Fig. 9 as function of number of load cycles.

4.2 Comparison stress intensity factor between experimental and numerical result

Fig. 12 Stress intensity factor ranges versus crack growth rate for the nickel CCT specimen without hole


Stress intensity factor and crack growth rate obtained from FEM and experiments, respectively, are used in obtaining the Paris law parameters - c and m and are shown in Fig. 12. Fig. 13 shows the variation of stress intensity factor along a half crack length, a, for three cases. There are three curves. These are based on theoretical approach by Isida, FEM analysis, and calculation back of stress intensity factor by Paris law equation (2), respectively.

da / dN = C (DK ) m

(2)

Isida’s solution about CCT is fundamentally relevant to metallic materials. However, for a short length crack, Isida’s approach can be used in nickel foam as well. Fig. 15 Comparison between experimental and FEM results for a nickel CCT specimen with 2 hole

Fig. 13 Comparison between Isida’s, experimental and FEM results of stress intensity factor along a half crack length for a nickel CCT specimen without hole

Fig. 16 Comparison between experimental and FEM results of stress intensity factor along a half crack length for a nickel CCT specimen with 2 hole

4.2.2 Result of CCT specimen with 2 holes In case of 2-hole specimen (Fig. 5), crack propagates more quickly than CCT specimen as shown in Fig. 14, due to geometrical influence.

4.2.3 Result of CCT specimen included with 4 holes In the case of 4-hole specimen shown in Fig. 6, crack propagates more quickly than any other previously described cases. Fatigue fracture behavior of a nickel foam specimen with 4-hole is shown in Fig. 17 (left).

Fig. 14 Fatigue fracture in 2-hole specimen (left) and FEM stress analysis (right) results in mode I direction of fatigue fracture with 2hole

The effect of holes at the crack propagation direction is that the hole absorbs crack even when the crack propagation direction is changed. Fig. 15 and Fig. 16 show the comparison of stress intensity factor between FEM solution and experimental calculations. FEM results are slightly lower than the experimental values. However, they are in the range for comparison.

Fig. 17 Fatigue fracture in 4-hole specimen (left) and FEM stress analysis (right) results in mode I direction of fatigue fracture with 4hole Remarkable finding in this case is the crack retardation effect. This is induced by a stress distribution around the holes. Further, in a 4-hole specimen stress intensity factor is relatively lower than 2-hole specimen even though propagation is faster. Stress intensity factor variation under fatigue cycles and in a half crack length is shown in Fig. 18 and Fig. 19, respectively.


2. Grenestedt, J. L., "Influence of Wavy Imperfections in Cell Walls on Elastic Stiffness of Cellular Solids," Journal of the Mechanics and Physics of Solids, Vol. 46, pp. 29-50, 1998. 3. Anderson, T. L., "Fracture Mechanics: Fundamentals and Applications," CRC Press, 1995. 4. Norman, E. D., "Mechanical Behavior of Materials : Engineering Method for Deformation, Fracture, and Fatigue," Vol. 2, pp.357558, 1999. 5. Bannantine, J. A., Comer, J. J., Handrock, J. L., "Fundamentals of Metal Fatigue Analysis," Prentice-Hall, 1989. 6. Paul, A., Seshacharyulu, T. and Ramamurty, U., "Tensile Strength of a Closed-Cell Al Foam in the Presence of Notches and Holes," Scripta Materialia, Vol. 40, No. 7, pp. 809-814, 1999. Fig. 18 Comparison between experimental and FEM results for a nickel CCT specimen with 4 hole

7. Kwak, D.S., Kim, S.H. and Oh, T.Y., "Effect of a Single Applied Overload on Fatigue Crack Growth Behavior in Laser-welded Sheet Metal," International Journal of Precision Engineering and Manufacturing, Vol. 7, No.3, pp. 30-34, 2006. 8. Park, U. H., Lee, H. W., Kim, S. J., Lee, C. R., Kim, J. H., "Stochastic Characteristics of Fatigue Crack Growth Resistance of SM45C Steel," International Journal of Automotive Technology, Vol. 8, No.5, pp. 623-628, 2007. 9. Yongming, L. and Sankaran, M., "Fatigue Limit Prediction of Notched Components Using Short Crack Growth Theory and an Asymptotic Interpolation Method," Engineering Fracture Mechanics, 2008 (In Press). 10. Cho, J. U., Lee, O. S. and Kim, S. C., "Fatigue Crack Propagation between Holes and Particles," International Journal of Fracture, Vol. 56, pp. 299-316, 1992.

Fig. 19 Comparison between experimental and FEM results of stress intensity factor along a half crack length for a nickel CCT specimen with 4 hole

5. Conclusion Following conclusions can be drawn from the experimental and numerical calculations on nickel foam. 1.

2.

3.

Paris law parameters such as c, and m, are used here to characterize the high strain rate fatigue behavior of nickel foam. Stress intensity factor range obtained from FEM analyses falls within the range of experimentally obtained values. In case of 2-hole specimen, crack propagation is faster than the no-hole case. Crack is towed into hole side as the influence of stress concentration at the side of hole increases. In the case of 4-hole specimen, crack propagates more quickly than any other cases. Due to the influence of compressive stress between 2-hole, crack closure has occurred. Therefore the propagation of crack initiated from the center has to retard or stop.

ACKNOWLEDGEMENT This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0075368).

REFERENCES 1. Sugimura, Y., Meyer, J., He, M. Y., Bart-Smith, H., Grenestedt, J. and Evans, A. G., "On the Mechanical Performance of Closed Cell Al Alloy Foams," Acta Materialia, Vol. 45, pp. 5245-5259, 1997.

11. Brown, W. F. and Srawley, J. E. after Isida, M., "Plain Strain Crack Toughness Testing of High Strength Metallic Materials," ASME, Special Technical Publication, No. 410, 1966.