ABSTRACT
Experimental study was performed to investigate the fracture behavior of relatively brittle polymer foam. A single notch bending specimen made of a PVC core cell foam A-series, A 800 and A 1200, are used for the investigation. To measure the strain around the defect section, a 2D digital image correction (DIC) technique was used. The fracture initiation toughness was calculated from the load displacement curve and a strain fields obtained from DIC technique. Furthermore a study was performed to investigate the failure behavior of foam core with sharp cracks, notch and circular hole. To reduce the size effect, the net cross-sectional areas of the specimen for all the geometries considered are kept constant. An Instron tensile loading machine was used and the tensile load was measured directly through the load cell. The full strain field around the section was measured using DIC and the data points at the interest location were extracted. The result was compared with the dog-bone tensile experiment of intact specimen. It was observed that, the net section strength for specimen with cracks, notch and circular hole is higher than that of the intact foam core.
INTRODUCTION
Lightweight structures with superior blast mitigation and impact resisting behavior are currently attracting the attention of Aerospace, Navy and other related industries. Sandwich structures with layer of composites as face sheets and foam material as core are widely used in such applications. Polymer foams have shown promising results as a core material for sandwich structures due to their high energy absorption capabilities, especially in the case of impact loading [1, 2]. There are well documented studies on the compressive properties and energy absorbing behavior of these materials [3]. It is shown that the structural response of polymer foam strongly depends on the foam density, cell microstructure and solid polymer properties [3]. Recent developments in manufacturing processes of polymer foams make the material available to be used in different shapes and sizes. Some of the applications of this material require these materials to have cuts and holes in them. It is well understood that, in the case of a fully dense material, the presence of a cracks, notches and holes in structures results in a stress concentration and thus leading to fracture. Understanding the tensile strength, the effect of notches and cracks and fracture behavior of foams is important to design structures using this material.
There exist a few studies on the tensile properties of open and closed cell foams with a presence of notches and holes. Andrews and Gibson [4], present a finite element analysis on the influence of defect size and cell size on the tensile strength of ductile two-dimensional cellular structures. Based on their study, they have concluded (a) the net section strength of a honeycomb with a circular hole is equal to the tensile strength of the intact honeycomb, (b) The net section strength of a honeycomb with a crack (defect width smaller than the cell size) is greater than the tensile strength of the intact honeycomb and the strengthening becomes more significant as the normalized cell size is increased, (c) the net section strength of a honeycomb with a notch (defect width greater than the cell size) is greater than the tensile strength of the intact honeycomb and the strengthening effect is independent to the normalized cell size.
In a different study, Andrews and Gibson [5] investigated, experimentally and numerically, the influence of crack-like defects on the tensile strength of open cell aluminum foam. They concluded that, the net section strength increased with an increasing notch size, indicating a notch strengthening effect. On the other hand, Paul et al. [6], experimentally studied the tensile strength of a closed cell Aluminum foam in the presence of notches and holes. They observed that, the net strength decreases with an increase in the notch length or holes diameter when the notch root or hole diameter is larger than the cell size.
Besides these few studies presented in literature, the effect of holes, cracks and notches in foam materials is not well understood. A detailed investigation on the failure of polymer foam and the effect of hole and cracks on the tensile strength of this material is essential. It is also observed that, foam cracking is one of the main failure modes in sandwich structures and understanding the fracture properties this material is important. Usually, in sandwich structures, the cracks starts at the core material and propagates to the faces and results in delimitation.
In this paper, an experimental investigation on the tensile properties of PVC foam with a presence of crack, notches and holes is presented. Furthermore, a fracture behavior of this material is investigated. An INSRON tensile testing machine in conjunction with a 2D digital image correlation (DIC) technique is used. It is observed that the net section tensile yield strength in the presence of holes, notches and cracks is higher than that of the intact specimen. It is also observed that, the defected specimen failed at a lower strain compared to the intact specimen, indicating a presence of a strain concentration around the defects section.
MATERIAL AND SPECIMEN GEOMETRY
The foam materials used in the present study is Corecell™ A series styrene foams, which are manufactured by Gurit SP Technologies specifically for marine sandwich composite applications. The material properties for A800 and A1200 CorecellTM foam that were used in the present study are listed in Table 1.
For the tensile experiments, four different specimen geometries, as shown in Fig.1, were considered; Dog-bone specimen without a defect (DB), with a center crack (CC), with an edge crack (EC) and with a center hole (CH). To avoid the size effect, the net cross sectional area were kept constant for all the specimens with defects considered. The gage lengths were 134 mm, widths were 25.4 mm, effective widths were 18 mm, and thicknesses were 6 mm.
Table 1 Selected mechanical properties of foam
|
Material |
Nominal density |
Shear modulus |
Shear Elongation |
|
|
(kg/m3) |
(MPa) |
(%) |
|
A800 |
150 |
47 |
50 |
|
A1200 |
210 |
76 |
46 |
Fig 1 Schematic drawing and geometry of tensile specimens, (a) Dog-bone specimen without a defect (DB), (b) with a center hole (CH), (c) with a center crack (CC), (d) with an edge crack (CH)
For the fracture experiment, single edge notched bend (SENB) specimens, as shown in Fig.2, were prepared from A1200 foam sheet according to ASTM E3999. The span length was 50 mm, the width was w= 14 mm, the thickness was B=7 mm and the initial crack length was a= 7 mm. The crack was first machined with 1 mm thick blade and later the artificial crack was extended with razor blade.
Fig 2 Schematic drawing of a single edge notched bend (SENB) specimen
EXPERIMENTAL SETUP TENSILE STRENGTH
An INSTRON machine was used in a displacement control mode at a speed of 1mm/min and the tensile load was recorded directly by the load cell. To measure the strain fields around the required area, a 2D DIC technique was used. Digital images of the sample at several deformation steps were taken using a high speed CCD camera. The resolution of the images was 2048×2048 pixels. First, the displacement and strain field around the gage length were calculated and later the strains on the required field were extracted
FRACTURE BEHAVIOR
The fracture surfaces of tensile specimens of the polymer foam considered in this study show no evidence of gross yielding or necking. Hence the foam is relatively brittle and stress intensity factor was used as a parameter to determine the fracture behavior. There are different techniques developed for determining the stress intensity factors for brittle materials. In the present study, the stress intensity factor KI was obtained experimentally using a three point single notched bending experiment. An INSTRON machine was used in a displacement control mode at a cross head speed of 1mm/min and the load-displacement data was recorded directly by the load cell. Digital images of the sample at several deformation steps were taken using a high speed CCD camera. A 2D DIC technique was used to obtain the displacement and strain fields. The stress intensity factor KI was calculated using three different techniques; critical load in the load-displacement curve using the linear elastic fracture mechanics theory, the stress intensity factor formulation using a single strain data point with a three parameter solution described by Dally and Sanford [7] and the modified multipoint strain method presented by Berger and Dally [8].
The detailed analysis of the above techniques can be obtained in the literature and only a brief description is presented below.
LOAD-DISPLACEMENT
The stress intensity factor K is calculated from the critical load in the load displacement curve using the linear elastic fracture mechanics given by Eq (1).
Where P is the critical load, a is the crack length, B is the thickness, W is the width, and S is the span.
SINGLE POINT THREE-TERM SOLUTION
A method for determining the mode I stress intensity factor by using a strain gage was first proposed by Dally and Sanford (1985). In this method a single or two strain gages will be placed on a region where the strain fields can be described by a three or four term of series. In the case of three-term series representation, only a single strain gage is required positioned near to the crack tip and oriented at a specific direction. The orientation angle a, of the strain gage is a function of material Poison’s ratio (v) and can be given as,
The location of the strain gage from the crack tip direction can be represented by the radius ( r) and angle (0). This angle is unique and related to a as shown below
The stress intensity factor can be given as
Where, E and are the Young’s modulus and Poison’s ratio of the material and is the strain in the radial direction
The Poison’s ratio of the foam used for the current experiment was determined from uniaxial tensile test. A dog-bone specimen was loaded uniaxially and using the DIC technique the three strain components; ex, ey and exy, at the center of the gage length were determined and these value were used to obtain the poison’s ratio using equation below.
DIGITAL IMAGE CORRELATION
Usually a single strain gage positioned in a specific direction is used to determine the fracture stress intensity factor using a three term solution [7]. However it is very difficult to put a strain gage on foam materials and get a correct strain signal. Furthermore, the strain gage only gives a single data point and it is very sensitive to the direction of the gage position. To avoid this problem a digital image correlation technique is used. In these fracture tests, the foam specimen only undergoes small amount of deformation before failure and the out-of-plane deformation is negligible. Therefore, the tests are considered as a 2-D and only a single camera is used to record the images. Digital images of the sample at several deformation steps were taken using a high speed CCD camera. A 2D digital image correlation (DIC) technique was used to obtain the displacement and strain fields.
In the case of a single strain gage technique, usually a prior knowledge of the plastic zone is required to accurately determine stress intensity factor from a single point value. However, in the current study, a series of single points are considered, and hence knowledge of the plastic zone prior to the experiment was not important. First the full strain field around the crack tip was generated, and then strain data at different radius were considered and used to calculate the stress intensity factor.
MULTIPLE POINT MANY-TERM SOLUTION
An overdeterministic approach to determine the stress intensity factor from many-term solution by using multiple strain gages proposed by Berger and Dally [1988] was adapted and used in the present study in conjunction with multiple strain values obtained from the DIC. The technique allows considering a larger number of strain points at a location far from the crack-tip where the plastic-zone correction is negligible and many terms in order to account for the higher order terms.
Unlike multiple strain gages, the DIC technique is full field and makes choosing strains at any location easy. Furthermore, since the three direction strain fields can be obtained at each point, a transformation of the strain field equations to the radial direction is not required. In the present study, a six term series expression of strain field was considered. The stress intensity factor is give by the relation
Where A0 is the first order coefficients
A large number of points were considered and the unknowns were solved using a least-squares approach.
