Plane stress fracture

Fracture toughness, essential work of fracture, plane stress, viscoelasticity, thin films, poly(ethylene-terephthalate). 

There is, however, no generally accepted theory for predicting the brittle-ductile transition or relating it to other properties of the polymer, although for some polymers it is closely related to the glass transition. The type of failure is also affected by geometrical factors and the precise nature of the stresses applied. Plane-strain conditions, under which one of the principal strains is zero, which are often found with thick samples, favour brittle fracture. Plane-stress conditions, xmder which one of the principal stresses is zero, which are often found with thin samples, favour ductile fracture. The type of starting crack or notch often deliberately introduced when fracture behaviour is examined can also have an important effect ... 

When plastic deformation occurs, crystallographic planes sHp past each other. SHp is fackitated by the unique atomic stmcture of metals, which consists of an electron cloud surrounding positive nuclei. This stmcture permits shifting of atomic position without separation of atomic planes and resultant fracture. The stress requked to sHp an atomic plane past an adjacent plane is extremely high if the entire plane moves at the same time. Therefore, the plane moves locally, which gives rise to line defects called dislocations. These dislocations explain strain hardening and many other phenomena. 

When a craze occurs around a rubber droplet the droplet is stressed not only in a direction parallel to the applied stress but also in the plane of the craze perpendicular to the applied stress (see Figure 3.9). Such a triaxial stress leading to dilation of the particle would be resisted by the high bulk modulus of the rubber, which would thus become load bearing. The fracture initiation stress of a polyblend should not therefore be substantially different from that of a glass. 

Eq. (13.145) is called the Griffith equation for thin sheets, i.e. in plane stress, where Gic, known as the fracture energy, has replaced 2y. A frequently used parameter in plane stress is the critical stress energy factor Kq, which in the case of a wide sheet (plane stress) is defined as... 

The equations above are valid for plane-stress situations, i.e. for thin sheets. For thicker sheets plain-strain conditions occur at the crack tip. In that case for a thick plate of infinite width containing a crack of length 2a the fracture stress is... 

According to Eqs. (13.145) and (13.148) the fracture stress in plane strain is a factor 1 /(1-v2) 1 /0.84 1.2 higher than in plane stress. Experimentally, however, the difference is much bigger. The reason for this discrepancy is that Griffith s equations were developed in linear fracture mechanics, which is based on the results of linear elasticity theory where the strains are supposed to be infinitesimal and proportional to the stress. 

In the case of thin sections the measure of toughness is given by plane-stress fracture toughness, Kc and elastic-plastic fracture mechanics (EPFM) are used. It is also necessary to bear in mind that plane-stress fracture toughness Kc is higher than plane-strain fracture toughness Xlc. 

Kc and Gc are the parameters used in linear elastic fracture mechanics (LEFM). Both factors are implicitly defined to this point for plane stress conditions. To understand the term plane stress, imagine that the applied stress is resolved into three components along Cartesian coordinates plane stress occurs when one component is = 0. Such conditions are most likely to occur when the specimen is thin. 

The parameters which apply to plane strain fracture are G c and Ki, where the subscript 1 indicates that the crack opening is due to tensile forces. K]c is measured by applying Eq. (11-52) to data obtained with thick specimens. To illustrate the differences between plane stress and plane strain fracture modes, thin polycarbonate specimens, with thicknesses <3 mm reported to have G values of 10 kJ/m, while the Gic of thick specimens is 1.5 kJ/m. ... 

In PEI the DCG process, as in any polymer, is active. The epsilon CTPZ, however, was not observed. No plane strain shear bands have yet been observed. Some form of localized crack tip shear process can be activated, however, as evidenced by the inversion transition that occured at higher stresses (at the higher temperatures). The fracture surface did not show fracture to occur on a slanted 45 degree plane. The fracture plane was still normal to the leading direction. The fracture surface, however, was not smooth, as seen with craze fracture, but has a definite roughened texture which is associated with active localized shearing. This texture is often described as honeycomb or tufted. 

Looking at the fracture surfaces of a thin sample in detail, it is noted that even in such ductile fracture the crack does not start from the notch tip but emanates from the region in advance of the notch tip where plane stress yielding is small. Figure 3... 

The brittle-ductile transition temperature depends on the characteristics of the sample such as thickness, surface defects, and the presence of flaws or notches. Increasing the thickness of the sample favors brittle fracture a typical example is polycarbonate at room temperature. The presence of surface defects (scratches) or the introduction of flaws and notches in the sample increases Tg. A polymer that displays ductile behavior at a particular temperature can break in the brittle mode if a notch is made in it examples are PVC and nylon. This type of behavior is explained by analyzing the distribution of stresses in the zone of the notch. When a sample is subjected to a uniaxial tension, a complex state of stresses is created at the tip of the notch and the yield stress brittle behavior known as notch brittleness. Brittle behavior is favored by sharp notches and thick samples where plane strain deformation prevails over plane stress deformation. 

RATE AND TEMPERATURE EFFECTS ON THE PLANE STRESS ESSENTIAL WORK OF FRACTURE IN SEMICRYSTALLINE PET... 

Aim of this paper is to investigate if the rate and temperature effects on the fracture parameters obtained by the EWF approach under plane stress condition are in some way related to the viscoelastic nature of the selected material (semicrystalline PET). 

Both criteria are exemplified in Table 2 and 3 for iPP/EPR-1 tested at room temperature. Table 2 shows (i) to be violated when the mode of failure is ductile (i.e at 0.001 m/s), whereas it remains valid, as expected, in case of brittle fracture (i.e 6 m/s). Table 3 highlights that plane stress conditions prevail roughly up to speeds higher than one decade of test speed tthan the ductile-brittle transition. 

Fig. 3. (i) Normal stress towards the fracture plane in mode 1 for an elastic material (ii) redistribution of stress by development of a plastic zone in front of a crack tip according to Irwin. 

Since the containers are made of thin blow-moulded material, it was decided to use conventional essential work of fracture (EWF) tests to obtain the plane stress fracture properties. More details about the EWF theory and its applications can be found in the ESIS protocol [8], and other publications [9-12],... 

Figure 8 shows a set of load-displacement curves for HM5411EA tested at 1 mm/s. Following the EWF procedure, the plot of the specific work of fracture, uy vs. ligament length, / is produced (Fig.9). It can be seen that linear approximation fits the data very well. From the Intercept between the fitted line and the y-axes, the value of 25.18 kJ/m is obtained for the essential work of fracture. This value represents fracture toughness under plane stress conditions. The slope of the linear fit represents the plastic work dissipation factor, Pwp, where is a shape factor associated with the shape and size of the plastic zone, and Wp is the plastic work dissipation per unit volume of material. The values of fiwp for all cases are given in Table 1.

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