Ductile behavior

Figure 1. Phase diagram of the Ti - H system. Points are related to the anomalous ductility behavior.

Other ductility behavior showed alloys with x = 1-25 and 1.54 whose ductility A (T) jumped near 300°C, passed through a maximum at about 350°C, passed through a maximum at about 350°C, and again decreased at higher test temperatures. Points in Fig. 1 correspond to temperatures of anomalous Au(T) behavior for appropriate hydrogen contents. A clear correlation is observed between the ductility anomalies and special lines in the phase diagram, it i.e., all points fall at the boundaries of the two-phase regions or at the line equidistant from these boundaries. 

The mass fraction crystallinity of molded PHB samples is typically around 60%. As shown in Table 3, PHB resembles isotactic polypropylene (iPP) with respect to melting temperature (175-180°C), Young s modulus (3.5-4 GPa) and the tensile strength (40 MPa). In addition, the crystallinity of iPP is approximately 65% [18]. Accordingly, the fracture behavior of PHB may be anticipated to be tough at room temperature. Molded PHB samples do indeed show ductile behavior, but over a period of several days at ambient conditions, they slowly become more brittle [82, 85, 86]. Consequently, the elongation to break of the ultimate PHB (3-8%) is markedly lower than that of iPP (400%). 

The allowable stress for occasional loads of short duration, such as surge, extreme wind, or earthquake, may be taken as the strength reduction factor times 90% of the yield strength at temperature times Mj for materials with ductile behavior. This yield strength shall be as listed in ASME BPV Code Section II, Part D, Table Y-l (ensure materials are suitable for hydrogen service see API 941), or determined in accordance with para. 

Despite the similarities in brittle and ductile behavior to ceramics and metals, respectively, the elastic and permanent deformation mechanisms in polymers are quite different, owing to the difference in structure and size scale of the entities undergoing movement. Whereas plastic deformation (or lack thereof) could be described in terms of dislocations and slip planes in metals and ceramics, the polymer chains that must be deformed are of a much larger size scale. Before discussing polymer mechanical properties in this context, however, we must first describe a phenomenon that is somewhat unique to polymers—one that imparts some astounding properties to these materials. That property is viscoelasticity, and it can be described in terms of fundamental processes that we have already introduced. 

The transition metal carbides do have a notable drawback relative to engineering applications low ductility at room temperature. Below 1070 K, these materials fail in a brittle manner, while above this temperature they become ductile and deform plastically on multiple slip systems much like fee (face-centered-cubic) metals. This transition from brittle to ductile behavior is analogous to that of bee (body-centered-cubic) metals such as iron, and arises from the combination of the bee metals strongly temperature-dependent yield stress (oy) and relatively temperature-insensitive fracture stress.1 Brittle fracture is promoted below the ductile-to-brittle transition temperature because the stress required to fracture is lower than that required to move dislocations, oy. The opposite is true, however, above the transition temperature. 

Time and energy can be saved if one recognizes that there is only one qualitative difference between a linear and a tridimensional polymer the existence in the former and the absence in the latter of a liquid state (at a macroscopic scale). For the rest, both families display the same type of boundaries in a time-temperature map (Fig. 10.1). Three domains are characterized by (I) a glassy/brittle behavior (I), (II), a glassy/ductile behavior, and (III) a rubbery behavior. The properties in domain I are practically... 

At room temperature, well below Tg, a brittle failure is generally observed. The ductile behavior appears when yielding becomes a competitive mechanism of deformation. At high speeds the brittle stress is not too much affected but ductile-brittle transition to higher temperatures. 

Figure 11. Brittle-ductile behavior of a series of methyl methacrylate/ethyl acrylate copolymers.

Fig. 5 Evolution of the fracture energy, Gtot, with the temperature, T, for non-nudeated and /S-nucleated resins with different flowabilities a MFR 0.3 dgmin-1 and b MFR 2 dgmin-1. The ductile-brittle transition temperature was chosen in a somewhat arbitrary manner as the temperature corresponding to half of the maximum of Gt01 in the considered MFR range. It reflects the transition from a semi-ductile to a fully ductile behavior, without breaking of the tested specimen. The test speed was about 1.5 ms-1, the specimens were injection molded...

A ductile behavior accounting for intense shear yielding. It is characterized by stable crack propagation, entire stress-whitening of the fracture surface and is accompanied by more or less pronounced shear lips. 

Amorphous polymers exhibit two mechanisms of localized plasticity crazing and shear yielding. These are generally thought of separately, with crazing corresponding to a brittle response while shear yielding is associated with ductile behavior and the development of noticeable plastic deformation prior... 

Finally, when the material is melted and crystallized, the material is tough and ductile compared with the single-crystal material. Therefore, this analogy is useful to understand the hypothesized transition from brittle to ductile behavior based on increased crystalline-amorphous interactions. 

Both banded (Tc = 52°C) and unbanded (Tc = 60°C) spherulitic morphologies had essentially identical stress-strain curves despite a difference in crystallinity of 8% and variations in spherulite size for these two crystallization conditions. These changes in crystallinity and spherulite size might compensate sufficiently to allow similar bulk deformation behavior. However, the sample crystallized at 52 °C should have smaller spherulites and thinner lamellae than the sample crystallized at 60 °C because of a greater probability of tie molecules. This, combined with its lower crystallinity, should allow more ductile behavior for the 52° C crystallized sample. The fact that both specimens deform similarly indi-... 

Tphe literature is replete with examples showing that the application of hydrostatic pressure enhances the ductile behavior of strained amorphous polymers. In this paper we present a possible explanation of this effect and two experiments demonstrating the enhanced ductility of polymers under compressive shear stresses applied orthogonally to the plane of shear. 

Lately, however, some surprising exceptions have been found to the general rule of low plasticity in ceramics. One is the perovskite oxide strontium titanate, SrTiOs. Recent studies on single crystals have revealed a transition from nonductile to ductile behavior in this material not only at temperatures above 1000°C, but again, below 600°C. Even more unexpectedly, it reached strains of 7 percent at room temperature with flow stresses comparable to those of copper and aluminum alloys. At both the high and low temperatures, the plasticity appears to be owing to a dislocation-based mechanism (Gumbsch et al., 2001). 

Above about 45°C, however, considerable yielding can be observed. Note that the transition between brittle and ductile behavior occurs at a temperature that is significantly below the T. Various theories have been advanced to explain yielding phenomena in polymers, some involving free volume arguments while others involve various types of molecular motion. As far as we can make out, none of these are entirely satisfactory and we won t discuss them here. Instead, we will finish off our discussion of stress/strain behavior by considering rubber elasticity. 

To design a resin with the property enhancements of AN without the cross-linking problem, it was found that SMA copolymers and terpolymers could be blended with ABS resins to form miscible blends with properties of HHABS. A fundamental look at the miscibility of SMA copolymers with SAN copolymers indicated that the optimum thermodynamic interaction occurs when the AN content of the SAN is nearly equal to the MA content of the SMA [72]. Kim et al. also found low impact strengths at all modifier levels when blending SMA with SAN-g-polybutadiene (GRC = grafted rubber concentrate) [73]. Blends of SMA with SAN and GRC (SAN + GRC = emulsion ABS) exhibited ductility behavior similar to HHABS. The impact strengths of the polymers were 2-5 ft-lb/in, in a notched Izod test at ambient temperature. 

It is worth noting that this semi-ductile behavior has been found in other polymers Newmann and Williams [4] observed stable crack propagation before brittle fracture in ABS over the temperature range from —40 to 0°C Bernal and Frontini also observed this type of behavior in a rubber-modified thermoplastic at room temperature [12]. 

When the material exhibits a ductile behavior in impact fracture, unstable fracture does not occur. The crack propagation is generally completely stable. 

To explain this inconsistency in the case of fracture with ductile behavior, another approach taking into account the crack initiation and crack propagation energies in the material is needed and has been proposed [18,19]. This approach assumes that the fracture energy of the polymer with ductile behavior varies linearly with crack extension and is given by... 

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