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Magnetic strips to simulate layered brittle solids in cleavage and fracture experiments
Acta Mechanica Solida Sinica, Vol. 21, No. 4, August, 2008 Published by AMSS Press, Wuhan, China. DOI: 10.1007/s10338-008-0839-9
ISSN 0894-9166
MAGNETIC STRIPS TO SIMULATE LAYERED BRITTLE SOLIDS IN CLEAVAGE AND FRACTURE EXPERIMENTS Francisco G. Emmerich1
Alfredo G. Cunha
Carlos M.A. Girelli
Arnobio I. Vassem
(Laboratory of Carbon and Ceramic Materials, Department of Physics, Universidade Federal do Espirito Santo, 29075-910 Vitoria-ES, Brazil)
Received 24 June 2008
ABSTRACT A characteristic of the fracture and cleavage experiments is that they are usually intrinsically destructive. Cracks do not completely heal in an unstressed system, even in crystals such as mica. Here, we used magnetic solids composed of magnetic strips for the non-destructive cleavage and brittle fracture experiments. Between the magnetic strips materials with different mechanical characteristics can be inserted, such as Teflon or foam strips, to change the mechanical properties of the solid. For the cleavage experiments, we developed an apparatus where parameters such as the main involved force can be measured easily. By inserting flaws, the magnetic solid can be used in dynamic fracture experiments, with the advantages of simulating macroscopically a non-destructive experiment in an easier way, that happen in real materials with much higher velocities. The apparatus and the used magnetic solid may be useful for demonstrations of fractures in classes.
KEY WORDS layered brittle solids, non-destructive measurements, cleavage, fracture
I. INTRODUCTION The measurement of material properties using non-destructive techniques, as described in the patents of Virdi[1] and Hutchinson and Langman[2] is of great interest. The fracture experiments are intrinsically destructive because cracks do not completely heal in an unstressed system, even in crystals such as mica[3] . Generally, there are difficulties in the reproduction of such events, especially in the case of the brittle solids, because the tensile strength depends on the details of the material texture and particularly of their flaws. Moreover, as shown by Fineberg[4] , Buehler et al.[5] , and Marder[6], the dynamics of the fracture is governed by the behavior of the material at the smallest scale around the tip of a flaw, but the experimental access to this region is usually an extremely difficult task because the zone sometimes approaches atomic dimensions and the fracture can occur very rapidly. Recently, Emmerich[7, 8] has addressed these questions, accessing experimentally the region where the rupture starts. He worked with a two-dimensional solid composed of unit cells formed by quadrupole magnets with foams glued on the inferior faces. The solid was disposed in a brick-wall pattern, with atomistic characteristics similar to the crack tip of brittle materials. Using an apparatus[9] , over which non-destructive fracture experiments were repeatedly performed.
Corresponding author. E-mail: [email protected] Project supported by the Brazilian agencies CNPq, CAPES and FINEP, and by Petrobras.
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ACTA MECHANICA SOLIDA SINICA
2008
Here, we will first work with experimental simulations of anisotropic layered structured brittle solids such as mica in cleavage experiments. We are particularly interested in the the Obreimoff’s experiment[10] on the cleavage of mica as discussed in another work[11] . However, since in isotropic crystalline materials, the ruptures tend to occur in certain specific crystalline planes[12] , the present work may be useful for experimental studies of the dynamics of brittle fracture[13] in brittle materials.
II. MAGNETIC LAYERED SOLID AND THE DEVELOPED APPARATUS[14] As shown in Figs.1 and 2, we have used a stacking of magnetic strips (1) with macroscopic transversal dimensions of the order of centimeters and the thickness of millimeter range. To avoid the influence of the gravitational forces (that applies in the vertical y-direction), the cleavage process takes place in a horizontal xz-plane. The cleavage process is realized through the application of a horizontal external force F perpendicular to the cleavage plane. The application of the force is through an inextensible cable (2) of fixed length and negligible weight, linked to a counterweight (3), through a fixed pulley (4) that is mounted on a rigid bar (5). The mass of the counterweight (280 g) was chosen so that the corresponding weight is superior to the maximum value of F . The counterweight lays horizontally on a digital balance (6), located on a movable plateau (7), which stays on a rigid horizontal surface (8). The movable plateau works as an elevator (jack), so that the counterweight can go up or down, making it possible to change the cleavage dimension d. c and F varies with each chosen value of d and h. The tension force F in cable 2 is obtained through the subtraction of the weight of the counterbalance (without tension in the cable (2)) and the digital balance during the experiment. To avoid the friction in the horizontal direction, which would affect the measurement of F , the part of the magnetic solid that is directly suffering the cleavage process has to be suspended. This is obtained by the use of an inextensible cable (9) of fixed length, that it is linked to a rigid bar (10). The other parts of the solid stay with their fixed layers in the xy-plane through rigid horizontal supports (11 and 12), made with non-magnetic material, which are linked to a rigid bar made with non-magnetic
Fig. 1. Photo of the developed apparatus for non-destructive experiments of cleavage similar to the Obreimoff’s experiment.
Fig. 2. Schematic diagram (from Ref.[14]) with the details of the developed apparatus for non-destructive experiments of cleavage similar to the Obreimoff’s experiment.
Vol. 21, No. 4
F.G. Emmerich et al.: Magnetic Strips to Simulate Layered Brittle Solids
· 335 ·
material (13). The magnetic strip (14) of the extremity of the magnetic solid adjacent to the rigid bar (13) has to be fixed to the rigid bar using, for example, epoxy glue. It can be convenient for many studies to add between the magnetic strips other materials with different mechanical characteristics, such as certain foams (low Young’s modulus) and certain low friction coefficient materials. In the case of present work, to reduce the mutual shear stress between the magnetic strips we used thin strips of Teflon (PTFE) between the magnetic strips.
III. RESULTS AND CONCLUSIONS We have conducted cleavage experiments. The dimension c and the force F with varying dimensions d and h are measured. The dimension d was varied using the elevator cursor. The distances were determined from photos taken with a digital camera, and the force F with the reading of the balance, discounting the counterweight. A millimeter ruler was attached to the apparatus to calibrate the distances. The results of some cleavage experiments are shown in Tables 1 and 2. In Fig.3, we have made a compilation of the results. We observed a decrease of the force F with the increase of d; however, the two used values of h produced similar values for F . Table 1. Experiments with values of F as a function of d for h = 13.7 mm
d (mm) 4.80 7.43 10.55 12.85 15.36 18.40 20.98 22.55
F (N) 1.111 1.033 0.937 0.856 0.775 0.729 0.694 0.672
d (mm) 4.63 7.21 9.88 12.45 15.50 18.08 21.18 22.34
F (N) 1.150 1.077 0.956 0.905 0.801 0.753 0.699 0.684
d (mm) 4.78 7.16 10.10 12.67 15.11 18.31 20.81 22.44
F (N) 1.209 1.160 1.054 0.941 0.831 0.797 0.738 0.709
Table 2. Experiments with values of F as a function of d for h = 17.4 mm
d (mm) 4.43 7.17 9.69 12.47 14.96 18.04 20.61 22.49
F (N) 1.150 1.101 1.037 0.966 0.886 0.792 0.753 0.734
d (mm) 4.48 7.24 10.00 12.79 15.36 17.82 20.69 22.19
F (N) 1.135 1.051 0.989 0.905 0.822 0.792 0.743 0.733
d (mm) 4.92 7.36 10.09 13.13 15.90 18.37 21.12 22.54
F (N) 1.157 1.096 0.974 0.888 0.826 0.783 0.765 0.737
In Fig.4 we show the details of one of the cleavage experiments. Since a previous reading of the counterweight on the balance was 281.3 g, the values of the cleavage parameters obtained directly from the figure are: F = 0.826 N, h = 17.4 mm, d = 15.9 mm and c = 150 mm. The conduction of fracture experiments similar to those performed by Emmerich[7] can be made directly and without difficulties with the magnetic strip solid. The procedures to perform dynamic fracture experiments with magnetic strip solids are being set up. In conclusion, we were able to carry out non-destructive and reproducible cleavage experiments. By inserting flaws (for example, by taking out part of a strip or by using an edge), the magnetic solid can be used in fracture experiments, determining the tensile strength and the speed of the crack propagation, with the advantages of being a non-destructive experiment. The configuration can be repeated in the
· 336 ·
ACTA MECHANICA SOLIDA SINICA
2008
Fig. 4. Top view photo showing the details of a nondestructive experiment of cleavage. Fig. 3. Force F as a function of d for the two used values of h in the cleavage experiments.
same way under the same conditions, and the experiment can simulates macroscopically easy observable events that happen in real materials with a much higher velocities.
References [1] Virdi,K.S., Non-destructive ultrasonic testing of structures to measure stress. UK Patent Application, GB 2 165 050 A, 1980. [2] Hutchinson,I.N. and Langman,R.A., Non-destructive determination of stress characteristics in magnetic materials. PCT/AU88/00293, WO 89/01613, 1989. [3] Lawn,B.R., Fracture of Brittle Solids, 2nd ed. Cambridge: Cambridge University Press, 1993. [4] Fineberg,J., Materials science: close-up on cracks. Nature, 2003, 426: 131-132. [5] Buehler,M.J., Abraham,F.F. and Gao,H., Hyperelasticity governs dynamic fracture at a critical length scale. Nature, 2003, 426: 141-146. [6] Marder,M., Effects of atoms on brittle fracture. International Journal of Fracture, 2004, 130: 517-555. [7] Emmerich,F.G., Direct experimental observation of a general pattern at the beginning of brittle fracture. Applied Physics Letters, 2005, 87: 131903. [8] Emmerich,F.G., Tensile strength and fracture toughness of brittle materials. Journal of Applied Physics, 2007, 102: 073504. [9] Emmerich,F.G., Apparatus for non-destructive experiments of brittle fracture and experimental simulation of earthquakes. Brazilian Patent Application, No.PI 0304992-2, 2003. [10] Obreimoff,J.W., The splitting of mica. Proceeding of the Royal Society of London, 1930, A127: 290-297. [11] Emmerich,F.G., Atomistic interpretation of the Obreimoff’s experiment. Eighth International Conference on the Fundamentals of Fracture — ICFF VIII, Hong Kong & Guangzhou, China, 2008. [12] Kelly,A. and Macmillan,N.H., Strong Solids, 3rd ed. Oxford: Clarendon Press, 1986. [13] Ravi-Chandar,K., Dynamic fracture of nominally brittle materials. International Journal of Fracture, 1998, 90: 83-102. [14] Emmerich,F.G., Cunha,A.G., Girelli,C.M.A. and Vassem,A.I., Apparatus with magnetic strips for nondestructive experimental simulation of cleavage and brittle fracture. Brazilian Patent Application, PI0800335-1, submitted to INPI, Brazil on 03 Jan 2008.
ISSN 0894-9166
MAGNETIC STRIPS TO SIMULATE LAYERED BRITTLE SOLIDS IN CLEAVAGE AND FRACTURE EXPERIMENTS Francisco G. Emmerich1
Alfredo G. Cunha
Carlos M.A. Girelli
Arnobio I. Vassem
(Laboratory of Carbon and Ceramic Materials, Department of Physics, Universidade Federal do Espirito Santo, 29075-910 Vitoria-ES, Brazil)
Received 24 June 2008
ABSTRACT A characteristic of the fracture and cleavage experiments is that they are usually intrinsically destructive. Cracks do not completely heal in an unstressed system, even in crystals such as mica. Here, we used magnetic solids composed of magnetic strips for the non-destructive cleavage and brittle fracture experiments. Between the magnetic strips materials with different mechanical characteristics can be inserted, such as Teflon or foam strips, to change the mechanical properties of the solid. For the cleavage experiments, we developed an apparatus where parameters such as the main involved force can be measured easily. By inserting flaws, the magnetic solid can be used in dynamic fracture experiments, with the advantages of simulating macroscopically a non-destructive experiment in an easier way, that happen in real materials with much higher velocities. The apparatus and the used magnetic solid may be useful for demonstrations of fractures in classes.
KEY WORDS layered brittle solids, non-destructive measurements, cleavage, fracture
I. INTRODUCTION The measurement of material properties using non-destructive techniques, as described in the patents of Virdi[1] and Hutchinson and Langman[2] is of great interest. The fracture experiments are intrinsically destructive because cracks do not completely heal in an unstressed system, even in crystals such as mica[3] . Generally, there are difficulties in the reproduction of such events, especially in the case of the brittle solids, because the tensile strength depends on the details of the material texture and particularly of their flaws. Moreover, as shown by Fineberg[4] , Buehler et al.[5] , and Marder[6], the dynamics of the fracture is governed by the behavior of the material at the smallest scale around the tip of a flaw, but the experimental access to this region is usually an extremely difficult task because the zone sometimes approaches atomic dimensions and the fracture can occur very rapidly. Recently, Emmerich[7, 8] has addressed these questions, accessing experimentally the region where the rupture starts. He worked with a two-dimensional solid composed of unit cells formed by quadrupole magnets with foams glued on the inferior faces. The solid was disposed in a brick-wall pattern, with atomistic characteristics similar to the crack tip of brittle materials. Using an apparatus[9] , over which non-destructive fracture experiments were repeatedly performed.
Corresponding author. E-mail: [email protected] Project supported by the Brazilian agencies CNPq, CAPES and FINEP, and by Petrobras.
· 334 ·
ACTA MECHANICA SOLIDA SINICA
2008
Here, we will first work with experimental simulations of anisotropic layered structured brittle solids such as mica in cleavage experiments. We are particularly interested in the the Obreimoff’s experiment[10] on the cleavage of mica as discussed in another work[11] . However, since in isotropic crystalline materials, the ruptures tend to occur in certain specific crystalline planes[12] , the present work may be useful for experimental studies of the dynamics of brittle fracture[13] in brittle materials.
II. MAGNETIC LAYERED SOLID AND THE DEVELOPED APPARATUS[14] As shown in Figs.1 and 2, we have used a stacking of magnetic strips (1) with macroscopic transversal dimensions of the order of centimeters and the thickness of millimeter range. To avoid the influence of the gravitational forces (that applies in the vertical y-direction), the cleavage process takes place in a horizontal xz-plane. The cleavage process is realized through the application of a horizontal external force F perpendicular to the cleavage plane. The application of the force is through an inextensible cable (2) of fixed length and negligible weight, linked to a counterweight (3), through a fixed pulley (4) that is mounted on a rigid bar (5). The mass of the counterweight (280 g) was chosen so that the corresponding weight is superior to the maximum value of F . The counterweight lays horizontally on a digital balance (6), located on a movable plateau (7), which stays on a rigid horizontal surface (8). The movable plateau works as an elevator (jack), so that the counterweight can go up or down, making it possible to change the cleavage dimension d. c and F varies with each chosen value of d and h. The tension force F in cable 2 is obtained through the subtraction of the weight of the counterbalance (without tension in the cable (2)) and the digital balance during the experiment. To avoid the friction in the horizontal direction, which would affect the measurement of F , the part of the magnetic solid that is directly suffering the cleavage process has to be suspended. This is obtained by the use of an inextensible cable (9) of fixed length, that it is linked to a rigid bar (10). The other parts of the solid stay with their fixed layers in the xy-plane through rigid horizontal supports (11 and 12), made with non-magnetic material, which are linked to a rigid bar made with non-magnetic
Fig. 1. Photo of the developed apparatus for non-destructive experiments of cleavage similar to the Obreimoff’s experiment.
Fig. 2. Schematic diagram (from Ref.[14]) with the details of the developed apparatus for non-destructive experiments of cleavage similar to the Obreimoff’s experiment.
Vol. 21, No. 4
F.G. Emmerich et al.: Magnetic Strips to Simulate Layered Brittle Solids
· 335 ·
material (13). The magnetic strip (14) of the extremity of the magnetic solid adjacent to the rigid bar (13) has to be fixed to the rigid bar using, for example, epoxy glue. It can be convenient for many studies to add between the magnetic strips other materials with different mechanical characteristics, such as certain foams (low Young’s modulus) and certain low friction coefficient materials. In the case of present work, to reduce the mutual shear stress between the magnetic strips we used thin strips of Teflon (PTFE) between the magnetic strips.
III. RESULTS AND CONCLUSIONS We have conducted cleavage experiments. The dimension c and the force F with varying dimensions d and h are measured. The dimension d was varied using the elevator cursor. The distances were determined from photos taken with a digital camera, and the force F with the reading of the balance, discounting the counterweight. A millimeter ruler was attached to the apparatus to calibrate the distances. The results of some cleavage experiments are shown in Tables 1 and 2. In Fig.3, we have made a compilation of the results. We observed a decrease of the force F with the increase of d; however, the two used values of h produced similar values for F . Table 1. Experiments with values of F as a function of d for h = 13.7 mm
d (mm) 4.80 7.43 10.55 12.85 15.36 18.40 20.98 22.55
F (N) 1.111 1.033 0.937 0.856 0.775 0.729 0.694 0.672
d (mm) 4.63 7.21 9.88 12.45 15.50 18.08 21.18 22.34
F (N) 1.150 1.077 0.956 0.905 0.801 0.753 0.699 0.684
d (mm) 4.78 7.16 10.10 12.67 15.11 18.31 20.81 22.44
F (N) 1.209 1.160 1.054 0.941 0.831 0.797 0.738 0.709
Table 2. Experiments with values of F as a function of d for h = 17.4 mm
d (mm) 4.43 7.17 9.69 12.47 14.96 18.04 20.61 22.49
F (N) 1.150 1.101 1.037 0.966 0.886 0.792 0.753 0.734
d (mm) 4.48 7.24 10.00 12.79 15.36 17.82 20.69 22.19
F (N) 1.135 1.051 0.989 0.905 0.822 0.792 0.743 0.733
d (mm) 4.92 7.36 10.09 13.13 15.90 18.37 21.12 22.54
F (N) 1.157 1.096 0.974 0.888 0.826 0.783 0.765 0.737
In Fig.4 we show the details of one of the cleavage experiments. Since a previous reading of the counterweight on the balance was 281.3 g, the values of the cleavage parameters obtained directly from the figure are: F = 0.826 N, h = 17.4 mm, d = 15.9 mm and c = 150 mm. The conduction of fracture experiments similar to those performed by Emmerich[7] can be made directly and without difficulties with the magnetic strip solid. The procedures to perform dynamic fracture experiments with magnetic strip solids are being set up. In conclusion, we were able to carry out non-destructive and reproducible cleavage experiments. By inserting flaws (for example, by taking out part of a strip or by using an edge), the magnetic solid can be used in fracture experiments, determining the tensile strength and the speed of the crack propagation, with the advantages of being a non-destructive experiment. The configuration can be repeated in the
· 336 ·
ACTA MECHANICA SOLIDA SINICA
2008
Fig. 4. Top view photo showing the details of a nondestructive experiment of cleavage. Fig. 3. Force F as a function of d for the two used values of h in the cleavage experiments.
same way under the same conditions, and the experiment can simulates macroscopically easy observable events that happen in real materials with a much higher velocities.
References [1] Virdi,K.S., Non-destructive ultrasonic testing of structures to measure stress. UK Patent Application, GB 2 165 050 A, 1980. [2] Hutchinson,I.N. and Langman,R.A., Non-destructive determination of stress characteristics in magnetic materials. PCT/AU88/00293, WO 89/01613, 1989. [3] Lawn,B.R., Fracture of Brittle Solids, 2nd ed. Cambridge: Cambridge University Press, 1993. [4] Fineberg,J., Materials science: close-up on cracks. Nature, 2003, 426: 131-132. [5] Buehler,M.J., Abraham,F.F. and Gao,H., Hyperelasticity governs dynamic fracture at a critical length scale. Nature, 2003, 426: 141-146. [6] Marder,M., Effects of atoms on brittle fracture. International Journal of Fracture, 2004, 130: 517-555. [7] Emmerich,F.G., Direct experimental observation of a general pattern at the beginning of brittle fracture. Applied Physics Letters, 2005, 87: 131903. [8] Emmerich,F.G., Tensile strength and fracture toughness of brittle materials. Journal of Applied Physics, 2007, 102: 073504. [9] Emmerich,F.G., Apparatus for non-destructive experiments of brittle fracture and experimental simulation of earthquakes. Brazilian Patent Application, No.PI 0304992-2, 2003. [10] Obreimoff,J.W., The splitting of mica. Proceeding of the Royal Society of London, 1930, A127: 290-297. [11] Emmerich,F.G., Atomistic interpretation of the Obreimoff’s experiment. Eighth International Conference on the Fundamentals of Fracture — ICFF VIII, Hong Kong & Guangzhou, China, 2008. [12] Kelly,A. and Macmillan,N.H., Strong Solids, 3rd ed. Oxford: Clarendon Press, 1986. [13] Ravi-Chandar,K., Dynamic fracture of nominally brittle materials. International Journal of Fracture, 1998, 90: 83-102. [14] Emmerich,F.G., Cunha,A.G., Girelli,C.M.A. and Vassem,A.I., Apparatus with magnetic strips for nondestructive experimental simulation of cleavage and brittle fracture. Brazilian Patent Application, PI0800335-1, submitted to INPI, Brazil on 03 Jan 2008.