FRACTURE BEHAVIOR AND MECHANICAL CHARACTERIZATION OF A COMPOSITE ORTHOPEDIC USE IN THE TWO DIRECTION

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FRACTURE BEHAVIOR AND MECHANICAL CHARACTERIZATION OF A COMPOSITE ORTHOPEDIC USE IN THE TWO DIRECTION

OF FLOW MOLDING

Sihem Achouri

Welding and NDT Research Center, Algiers (Chéraga)- Algeria csc.dz.

Civil Engineering Laboratory,

University of Badji Mokhtar Annaba, 23000 Annaba, Algeria.

Souma_sihem@yahoo.fr

Bachir Redjel

Civil Engineering Laboratory

University of Badji Mokhtar Annaba, 23000 Annaba, Algeria.

bredjel@yahoo.fr

Mounira Bourebia

mounirabourbia@gmail.com

D.Berdjane

berdjamel@yahoo.fr S.Bouhouche

bouhouche11@yahoo.fr

ABSTRACT—A standard tensile test was carried out on prismatic specimens of glass-perlon reinforced acrylic resin laminate composite material of orthopedic use, developed by the National Office Equipments and Accessories for People with Disabilities, ONAAPH Annaba (Algeria). The measurement results of the Young's modulus and the fracture strength show a large scatter characteristic of these materials and are influenced by the cutting direction of the samples compared to the direction of molding. The use of the probabilistic two parameters Weibull's model made it possible to characterize brittleness and the fracture behavior of these materials and quantitatively to describe the probabilistic aspect of the latter. A report of the principal mechanisms responsible of the fracture is drawed up according to microscopic observations of the fracture topographies of the broken samples.

Keywords—weibull, glass, perlon,acrylic, orthopedic.

I.INTRODUCTION

The analysis of the mechanical behavior of the laminate composite materials subjected to various solicitations remains very complex. This difficulty is mainly related to the often three-phase constitution of these materials (resin, fiber reinforcement, various additions) and to the complexity of the deformation mechanisms at the microscopic level (heterogeneity, anisotropy…) [1-2]. Many parameters such as the nature of constitutive materials or the stacking sequences thus influence the mechanical behavior of these materials which is highly depend on the level of damage [3-4-5].

Defects such as the porosities created when formatting depend amongst other things on the parameters of injection.

The law of Weibull on the statistical and probabilistic aspect of the materials fracture behavior is of general application.

Therefore the statistical approach of the fracture appears essential for the use of brittle composite materials. It involves a design completely different on the levels from the engineering and design offices and laboratories. The concept of absolute safety must be replaced by the concept of acceptable fracture probability [6]. The fracture probability is then a compromise between economic considerations and safety considerations and generally varies between 10^-3and 10^-7[7].

The goal of this specific work is to obtain an improved understanding on the mechanical characterization of an orthopedic use glass-perlon reinforced acrylic matrix laminate composite material and the probabilistic aspect of his failure. The application of the model of Weibull have been investigated to describe the fracture behavior of this laminate which was worked out by "national office of accessories and equipments for handicapped persons"

ONAAPH of Annaba (Algeria).

II. DESCRIPTION OF THE STATISTICAL MODEL OF WEIBULL

The model of Weibull is based on the principle of the concept of the weak link theory. The application of this model to a laminate composite material supposes that the fracture of an element of the structure leads to the instantaneous ruin of all the structure [8].

The failure probability Pfof a material of volume V subjected to constraints distribution σ is given by the equation(Eq1):

Pf = 1 – exp [-

∫

_V

f(σ) dv ] (1) Where:

σ is the applied stress.

Proceedings of the 2015 International Conference on Industrial Engineering and Operations Management Dubai, United Arab Emirates (UAE), March 3 – 5, 2015

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σ_u is the stress threshold below which the probability of failure is zero. Generally it is taken equal to zero in order to have a more consistent definition of the Weibull modulus and to increase the safety factor [9].

σ₀ is the standardization stress without physical significance which gives to unit volume a probability of failure of 0,632.

m is a the modulus or the coefficient of Weibull.

The two parameters m and σ0 are regarded as material properties. The parameter m is thus an empirical characteristic which represents the brittleness of material and also characterizes the width of the distribution of fracture stresses.

For a sample of volume Vt subjected to tensile stresses σt uniformly distributed, the equation (Eq.1) can be written:

Pf = 1 – exp [ - Vt(σt / σ0) ^m] (2) The index _t relates to tension.

The solution passes by assigning a stress level classified by ascending order from 1 to N, at the rank i, a failure probability Pf function of this rank through the estimator given by the following expression(Eq.3):

Pf = i / (N+1) (3) The determination of the parameter of Weibull consists on the linearization of the equation (Eq.2) of the probability of failure which can be written (Eq.4):

Ln.Ln [1/(1-Pf)] = m. Ln σt – m.Ln σ0 + Ln Vt (4) The representation of Ln.Ln [1/(1-Pf)] versus Ln σt is thus a straight line of slope m.

III. EXPERIMENTAL

The method of production adopted for the manufacturing specimens is the same one as that used in the manufacture of the prostheses. The material having been used for manufacture of the specimens is thus a laminate made up of glass E and perlon reinforcements and an acrylic resin and other additives that are an acceleration operator and a hardener. The stratification is limited to 6 plys for samples with reasonable thickness of approximately 3 mm.

The configuration considered is two perlon layers, two layers of glass and two perlon layers designated P-V-2P-V- P.

Fig.1. Production method for specimens.

The specimens were cut from molded plates using a special diamonds saw. Figure 2 shows typical specimen geometry which was prismatic form of 150 mm length, 10

mm width and 3 mm thick.

Fig.2. Tensile specimen.

The tests were carried out in monotonous tension on a controlab type machine of a capacity of 5 kN equipped with an automatic system of acquisition of the load-displacement curve during the loading at 5mm/min cross head speed until the total ruin (figure3).

Fig.3. Tensile test machine.

IV. RESULTS AND DISCUSSION A.Analysis of Mechanical Properties Measured

Figures 4 and 5 show examples of the evolution of the stress-strain curves for the two directions of cutting for the manufactured laminate composite.

Fig.4. Stress-strain curves in the direction perpendicular to the molding of the laminate P-V-2P-V-P

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Fig.5. Stress-strain curves for laminate P-V-2P-V-Pin the molding direction

The shape of the curves is overall similar for the two direction of cutting. These curves are linear elastic until failure signifying a completely brittle state in the case of the molding direction. For the samples cut in the direction perpendicular of the molding the curves after the linear elasctic behavior present a second part of the linearity which reflects the initiation and the accumulation of the diffuse and progressive damage that occurs within the structure before the total ruin. This is mainly caused by a multi matrix cracking, fibre-matrix debonding, delamination and pull out. The fracture is reached at the maximum load value corresponding to the saturation of the phenomenon of multi cracking.

Table 1 summarizes the average values of ultimate failure strengths and the elastic modulus measured of the laminate studied as well as the coefficients of variation expressed as a percentage between brackets.

TABLE 1 MEASURED MECHANICAL PROPERTIES OF THE STUDIED LAMINATE

Laminate P-V-2P-V-P

Feel Molding Perpendicular

(MPa) 26 (12%) 51 (15%)

E (MPa) 1295(19%) 1496 (14%)

As shown in table 1 the values of the measured mechanical properties are characterized by an allowed scatter accepted today as a characteristic of composite materials. It can be attributed to the presence of defects such as the bubbles and micro porosities (figure 6), to the formation of folds of reinforcement, to the weakness of the interface and to the heterogeneity of the microstructure.

Fig.6. Porosity of surface and interior.

An observation of the process of implementation also revealed a premature polymerization as well as differences in thicknesses on the same product as other defects. The presence of defects of various dimensions, shape and sizes randomly distributed at heart and on the surface of samples is at the origin of the failure of these materials. This one can be started at different stress levels according to the orientation, the localization, the dimension and the severity of these defects. Moreover the defects are generally randomly oriented compared to the applied stress. This random distribution of the defects accounts for the distribution of the values of failure strength observed in brittle materials

It has been shown from the measured results that the values of the strengths and the modulus measured in the direction perpendicular to the molding are higher than those measured in the direction of the molding. The histogram of figure 7 illustrates this aspect which shows clearly a significant difference.

Fig.7. Influence of molding direction on the mechanical characteristics of the laminate.

This difference is much more marked in the case of fracture stresses than in that of the elastic modulus. The relationship between the stress at failure in the direction of the molding and that in the perpendicular direction and that between the elastic modulus in the two directions of cutting are respectively a value of 0,51 and 0,87.These differences can be put in the active of the method of pulling of glass fiber which is a little free in the direction of the molding that in the direction perpendicular to this last. In addition the friction loads between the glass fibres in the nodes also

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contribute to amplify the phenomenon.

Fracture mode and damage mechanisms

The microscopic observations revealed that the tear follows the path of the nodes of glass fiber following a plane perpendicular to the axis of the applied load in the tensile test [10].

The fracture propagation is always accompanied by a change of aspect and a discolouration of the composite which turns to white color. This is probably the consequence of the first decohesions and the debonding due to the effect of the applied stress. The tear presents in general debonding of perlon and glass fibres. Other observations have located the fracture in spaces inter stratification and in fabric at the stitches (figure 8). Finally, note that the paths of cracking remain very complex to locate. An interesting study on the characterization of the woven structures helped advance information on the damage mechanisms of the fabrics [11]

Fig.8. Tensile breakage.

V. APPLICATION OF THE MODEL OF WEIBULL Figure 9 shows the failure probabilities for each stress level achieved in the tests for composite studied in the two directions of molding according to the applied stress. As it appears in the figures, these curves are the sigmoid ones translating the distributions of Weibull of failure stresses measured in tension.

Fig.9. Probability of fracture for each level of constraint for P-V-2P-V- Parchitecture in the two directions of molding

Figure 10 show the chart representation of the equation

of linear probability for determining the Weibull modulus and the standardization stress for the laminate tested in the two directions of cutting.

Fig.10. Chart of the equation of probability linear for P-V-2P-V- Parchitecture for the two directions of molding

There is a slight scatter of the experimental points around the straight linear regression lines in the two cases.

The existence of various types of defects probably leading to several distributions that determine the behavior of these materials is one of the causes of the deviations of the positions of the points compared to the line. The size of the defects affects the strength of these materials. Other variables such as the slow growth of the cracks, the important bifurcations of the cracking ways exist and accentuate the phenomena of scatter around the linear straight regression lines. In addition the multiple origins of the initiators of fracture in these materials and the various failure modes accentuate the phenomena of scatter and the differences noted.

Table 2 shows the measurement results of the Weibull's moduli of the studied laminate in the two molding directions.

TABLE 2 MEASURED VALUES OF THE MODULI OF WEIBULL Laminate Feel molding Feel perpendicular

P-V-2P-V-P 7,43 6,99

The laminate Weibul's moduli estimated from the slope of the linear straight regression lines of figure 7 are low and thus reflect the brittle character of these laminates.The Weibull's modulus in the direction of the molding is slightly higher than this in the perpendicular direction for the laminate. The difference is about 6% and cannot be significant.

The multiple origins of the initiators of fracture in these materials accentuate the phenomena of scatter from a direction of cutting to the other. The defects that have dramatic effect on failure stresses do not belong to the same statistical family and a mixture of two or several statistical families influences the calculated values of the modulus of Weibull.

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Many studies reported in the litterature have attempted to coreler the Weibull modulus to the measurement parameters of the scatter observed in the failure stresses of composite materials. L.J. Broutman & R.H. Krock [12]

estimate that for a coefficient of variation of 10%, the Weibull modulus is of the ordrer 10. C. Zweben [13]

connects inversely Weibull modulus m and the coefficient of variation C of failure stresses in tension of the composites by the relation : m = 1,2/C. The same relation was suggested by R.C. Wetherhold [14] who reported m values ranging between 12,9 and 16,6. J. Margetson & B.E.

Brokenbrow [15] propose the following relation: C = 1,27/(m + 0,56).

The values of the Weibull modulus m measured experimentally for the two directions and those calculated from the empirical relations mentioned above are summarized in table3.

TABLE 3 EXPERIMENTAL AND CALCULATED VALUES OF WEIBULL MODULUS

Laminate P-V-2P-V-P

feel Molding Perpendicular

σ [ MPa ] 26 (12%) 51 (15%)

m exp. 7,43 6,99

m (Zweben) 10 8

m(Margeston) 10,02 7,90

The relationship of C. Zweben and J. Margeston lead to calculated values of m comparable. These values are however higher than those measured by the experiment.

The difference is mainly due to the high degree of scatter observed on the measured values of failure stresses of the laminate. This scatter whose origins are multiple is the consequence of the presence of surface defects on the specimens skin and of volume defects at the heart of these last of various shapes, sizes, orientations and severities belonging to statistical populations not comparable. All these combined parameters cannot give an account of a good application of the correlations applied.

VI. CONCLUSION

This experimental work on the randomness of the tensile strength of laminated glass-fiber reinforcement to Perlon orthopedic allowed to describe the ruin by a statistical- probabilistic analysis based on the Weibull model with two parameters. Rupture is influenced by the heterogeneity of the structure which induces damage random phenomena and the variability of the mechanical properties. In this sense, the experimental results have established to formulate the following:

The results of measurement of the mechanical properties are characterized by a scatter mainly due to the heterogeneity of the laminate studied and to the presence of defects within the volume of the specimens.

These defects are introduced in various ways during development or during samples preparation. It appears that the values of failure stresses and elastic moduli measured in the direction perpendicular to that of the molding are greater than those measured in the direction of the molding.

The Weibull parameters in the perpendicular direction of the molding are appreciably close. However a scatter is observed in the values in the direction of the molding.

Tear has déchaussements fiberglass and perlon occurring without delamination of the matrix. This suggests one way that the fiber-matrix interface has a less strong than that of the matrix itself resistance.

ACKNOWLEDGMENT

The authors thank the national office for manufacture of the prostheses for handicapped ONAAPH Annaba (Algeria), the general direction of Algiers and the regional direction of Constantine for the facilities to supply components having been used for manufacture of the composite plates of this study.

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