Ductile To Brittle Transition Temperature

Interfacial and Nanoscale Fracture

Westward. Gerberich , W. Yang , in Comprehensive Structural Integrity, 2003

eight.01.iv.one.ane Breakable-to-ductile transition

The brittle-to-ductile transition is essential for the understanding of fracture processes. Experiments indicate that solids are brittle at very low temperature, and their toughness go much higher at elevate temperature. A lower shelf at low temperature, an upper shelf at loftier temperature, and a transition regime in a temperature range where the toughness changes rapidly characterize the toughness–temperature curve. Transition temperature is a critical mensurate for a structural fabric.

Besides temperature, strain charge per unit influences the fracture toughness. A faster strain rate likely induces brittle fracture. With other weather fixed, a slower loading rate leads to ductile fracture. The resemblance between the temperature effect and the charge per unit consequence is not casual. Temperature measures the mobility of atoms to change their configurations; the college the mobility, the more capable the solid to adapt a deformation field. The strain charge per unit, alternatively, defines the speed imposed on the deformation to a material. Their competition leads to the above-mentioned property of textile toughness.

Dislocation emission from a scissure tip dictates the brittle-to-ductile transition of materials (Kelly et al., 1967; Rice and Thomson, 1974; Schoeck, 1991; Rice, 1992; Rice and Beltz, 1994). The mechanics modeling of brittle vs. ductile behavior of a crystal started from the work of Rice and Thomson (1974). Their model is described in Figure fifteen. 2 events, cleavage and dislocation emission, are in competition.

Effigy 15. Competition between cleavage and dislocation emission, in spirit of Rice and Thomson (1974).

The glide planes of dislocations are unremarkably inclined to the cleavage path (Chiao and Clarke, 1989), and so that cleavage and dislocation emission are determined by different stress distributions. The cleavage along the crack extension line is driven by the applied stress intensity factor, and resisted past the surface energy for breakable fracture as

$\frac{1-{\nu }^{\mathrm{ii}}}{E}{K}^2={\gamma }_{\mathrm{cr}}$

while the driving strength for a dislocation emitted at an angle ϕ inclined with the crack is scaled with

$\frac{K}{2\sqrt{2}\pi r_0}\sin \mathit{\varphi }\text{cos}\frac{3}{2}\mathit{\varphi }$

and resisted by its gliding resistance ${\tau }_{\mathrm{cr}}$ .

If the cleavage proceeds before the emission of a dislocation, the crack will remain atomistically precipitous. Alternatively, dislocation emission along a aeroplane inclined to the crack extension line will blunt the crack, and lead to a tendency of ductile response. One has to introduce a cadre size for spontaneous dislocation emission to quantify the driving force. By thermal fluctuation that assists the dislocation to surpass an activation energy barrier, dislocation emission is possible even if the driving force falls slightly beneath the resistance. The Rice–Thomson theory quantified the ductility of many materials in terms of their cleavage vs. dislocation emission calculations. The theory, nevertheless, made several assumptions that attracted the subsequent improvements.

Rice–Thomson model assumed that the dislocation glide plane intersected with the crack front end. In the actual cases, more than one plane tin emit dislocations. The 3D configurations of these planes could twist from the scissure front by an angle. The 2d Rice–Thomson model may overestimate the energy barrier to nucleate a dislocation loop, and consequently underestimate the ductility. More rigorous analysis afterward on (Gao and Rice, 1989) studied the emission of a semi-elliptical loop. Their upshot confirmed that less energy is needed to nucleate a 3D loop. The Rice–Thomson model assumed that the dislocations emitted from the crack tip are consummate dislocations. Emission of partial dislocations are observed in materials such every bit b.c.c. crystals. The near critical problem of the Rice–Thomson model is the uncertain parameter, the dislocation core size r0, within the model. Subsequent accelerate of the Peierls dislocation model clarified this uncertainty.

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A Tribute to F.R.N. Nabarro

J. Bonneville , ... P. Guyot , in Dislocations in Solids, 2008

5.1.3.3 Brittle-to-ductile transition

As already mentioned the brittle-to-ductile transition of icosahedral quasicrystals is usually reported to occur at high temperatures (above 0.7 $T_{\mathrm{yard}}$ , $T_{\mathrm{m}}$ being the melting temperature). The results presented above show that, at low temperature, i-Al-Cu-Atomic number 26 has a very loftier yield stress and high hardness, which implies that crack initiation requires large stresses, whereas the depression $K_{\mathrm{IC}}$ value indicates that crack propagation takes place under depression stresses. As pointed out in [56], according to these criteria, i-Al-Cu-Fe tin can exist classified as intrinsically brittle. However, i-Al-Cu-Fe exhibits plastic deformation under complex stress conditions, as evidenced past the crack-free pyramid indentation under modest applied loads and pressure confining techniques.

For crystalline materials, deformed under abiding strain-charge per unit atmospheric condition, brittleness occurs when dislocation movements practice non compensate the applied strain rate, that is when dislocation mobility and/or mobile dislocation density are (is) too small. Covalent semiconductors, such every bit Si, which are grown almost dislocation-free, vest to the latter category. Silicon is brittle at room and intermediate temperatures and exhibits, similar Al-Cu-Iron, a large yield point in a higher place the BDT temperature, which is followed past a stage of work-hardening [61]. Omri et al. [62] showed, for Si, that the BDT temperature was shifted to lower temperatures if dislocations were introduced past a suitable pre-deformation at loftier temperatures. Like pre-straining experiments have been conducted by Giacometti et al. [63]. The stress–strain curve of a specimen initially pre-deformed at 650 °C up to most 5% plastic strain, $\sigma \approx 235\text{MPa}$ , i.east. at the expected maximum in dislocation density [64], and then farther strained at 450 °C, i.eastward. the everyman temperature of the BDT temperature interval is similar to the one of a specimen monotonically plain-featured at 450 °C. The pre-deformation does non significantly raise ductility and both specimens bankrupt very quickly later yielding. Like experiments were performed at 300 °C and 400 °C, starting from the same pre-deformed state at 650 °C. Identical results were obtained, although in these cases rupture occurs without any detectable plastic deformation. These experiments led Giacometti et al. [63] to conclude that the substructure, which is formed past pre-straining at high temperature, is essentially 'frozen' when the specimen is cooled beneath the BDT temperature, supporting the idea that the brittleness of Al-Cu-Atomic number 26 quasicrystals did not result from an insufficient density of the strain-carriers, but rather from their lack of mobility. Annotation that the terminology of strain-carrier was used instead of dislocation, because no direct proof of dislocation action was given in these experiments.

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Intermetallics: Nickel Aluminides

I. Bakery , E.P. George , in Encyclopedia of Materials: Science and Engineering science, 2001

1.5 The Upshot of Temperature on Ductility

NiAl alloys show quite marked brittle-to-ductile transitions at 500–600K, whose temperatures depend on strain charge per unit, composition, grain size, and orientation for single crystals (see Fig. 5). At higher temperatures, elongations of 60% can exist obtained, dislocation climb providing the additional deformation modes necessary for such ductility in polycrystals. Increases in strain rate shift the brittle-to-ductile transition to college temperature (come across Fig. five). For instance, a modify in strain rate of thou causes a shift of almost 200K in polycrystalline NiAl. The stoichiometric alloy, at least at big grain sizes, requires the highest temperature to become ductile, presumably owing to a lack of constitutional defects.

Effigy 5. Strain to failure for cast and extruded stoichiometric NiAl (open up symbols) and [001]-oriented unmarried crystals of Ni–50Al and Ni–60Al (filled symbols) every bit a part of temperature (later on Noebe et al. 1993).

Grain refinement tin essentially better ductility within the brittle-to-ductile transition window of 550–750K. For example, at 673K the ductility of polycrystalline Ni–49Al can be improved dramatically past reducing the grains to below a critical size (20μm) when tensile elongations of >40% are achieved. The critical grain size is largest for stoichiometric NiAl owing to lack of (hardening from) constitutional defects. Unfortunately, for Ni–49Al the disquisitional grain size appears to exist less than ∼4μm at room temperature. At higher temperatures, ⩾873K, the ductility is essentially contained of grain size.

The ductility of single crystals increases with increasing temperature and fifty-fifty hard 〈100〉 orientation single crystals tin can become ductile at >600K for the stoichiometric composition and >1000K for Ni–60Al, elongations of 90% being possible at college temperature. Strain charge per unit increases of two orders of magnitude shift the breakable-to-ductile transition temperature of hard orientation crystals by near 120K, i.due east., like to polycrystals, only other orientations appear to be more than weakly affected.

The fracture toughness of both single crystals and polycrystals shows a marked increase to a higher place 450–550K.

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Dislocations in Solids

Guanshui Xu , in Dislocations in Solids, 2004

vii Estimates of the brittle to ductile transition temperature

Following the viewpoint that the brittle to ductile transition in bcc transition metals, and particularly in α-Atomic number 26, is virtually likely controlled by the process of dislocation nucleation at crack tips, the preceding results can then be used to estimate the breakable to ductile transition temperatures attendant to the three nucleation modes considered. No precise experimental information on the transition temperature of single crystal α-Fe are available. The transition temperature for polycrystal low carbon steel is about 250 One thousand, every bit determined from Charpy bear on experiments [57]. In the absence of more direct measurements, we postulate the transition temperature for pure α-Fe to be in the range of 250–300 1000. A number of different scenarios may be constructed to draw a brittle to ductile transition. We consider here a relatively precise process described by Argon [7], in which a brittle cleavage crevice in α-Fe propagates up a temperature gradient with a given constant velocity u _c. Co-ordinate to the Arrhenius-type relation, the mean reciprocal activation time or activation rate of nucleation of a critical dislocation embryo from the crack tip is

(64) $\frac{1}{ta}={\mathrm{five}}_{\text{Yard}}exp\left(-\frac{\Delta U_{\text{act}}}{\mathrm{chiliad}{T}_{\text{BD}}}\right),$

where T _BD is the brittle to ductile transition temperature, k = ane.38 × 10⁻²³ J/K is Boltzmann constant, and v _Thou is the normal mode frequency of an cantlet cluster of the size R _d encompassing the saddle point configuration of the dislocation embryo at the crack tip, for which a good estimate should be

where v _D is the central atomic frequency (Debye frequency). When the residence time t _r of the traveling singular scissure tip field advancing with a velocity u _c over a distance of order R _d is equal to the mean activation time t _a in that location is high probability of the formation of a dislocation embryo of critical shape. Thus, when

(66) $t_{\text{r}}=\frac{R_{\text{d}}}{v_{\text{c}}}=t_{\text{a}}=\frac{1}{v_{\text{Yard}}}exp\left(\frac{\Delta U_{\text{act}}}{\mathrm{thou}{T}_{\text{BD}}}\right),$

the temperature along the crack path where this condition is met should be the breakable to ductile transition temperature if the germination of the disquisitional embryo also triggers the processes of the wholesale dislocation multiplication. And then the condition for the brittle to ductile transition becomes

(67) $\frac{{\mathrm{five}}_{\text{G}}{R}_{\text{d}}}{5_{\text{c}}}=exp\left(\frac{\Delta U_{\text{act}}}{\mathrm{yard}{T}_{\text{BD}}}\right).$

Recognizing

and defining the normalized activation energy

nosotros can recast the status for the breakable to ductile transition as

(lxx) $T_{\text{BD}}=\frac{\mu b^{\mathrm{iii}}}{k(\mathrm{ane}-\mathrm{five})}\frac{\gamma }{\text{In(}{\mathrm{five}}_{\text{S}}/v_{\text{C}})}.$

Here u _s is the velocity of a sound wave. If the temperature dependence of shear modulus is farther taken into account to the outset gild approximation through

where μ ₀ is the shear modulus at 0 Yard and η is typically of the order 0.5 for most metals, we find that

(72) $T_{\text{BD}}=T_0{\left[\frac{\text{In(}{5}_{\text{S}}/v_{\text{C}})}{\gamma }+\eta \frac{T_0}{T_{\text{m}}}\right]}^{-\mathrm{ane}},$

where T ₀ = μ ₀ b ^three/yard(i − v) = 1.2 × 10^five K, the melting signal T _m = 1809 G for α-Fe. The selection of the typical value u _c ∼ 1 cm/s results in ln(u _south/u _c) ∼ x.

The dependence of the activation energy for dislocation nucleation on the crack driving force is plotted in Fig. 56 for each of the iii modes of nucleation considered. The normalized activation energy γ at the disquisitional driving forcefulness for cleavage, i.eastward. at K _I/Chiliad _IC = 1, determines the transition temperatures through (72). This relation is plotted in Fig. 57, together with the estimates of transition temperatures associated with the three modes of nucleation.

Fig. 56. The activation energies for dislocation nucleation at a crevice tip in α-Fe for three different modes of nucleation.

Fig. 57. The estimated breakable to ductile transition temperatures in α-Fe.

Likewise shown in the figure is the value of the transition temperature for polycrystalline Fe. It is evident from this comparing that just nucleation on the cleavage ledge furnishes the transition temperature that is in the range of the expected value of α-Fe. The other two mechanisms grossly overestimate the transition temperature. These results strongly suggest that dislocation nucleation from the crack tip is an inhomogeneous procedure. The dislocation loops, which eventually shield the crack, are most likely emitted from the ledges distributed along the cleft front.

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Oxidation- and Corrosion-Resistant Coatings

Sudhangshu Bose , in High Temperature Coatings (Second Edition), 2018

Ductile-to-Brittle Transition Temperature

Both diffusion and overlay coatings exhibit low ductility below the DBTT, whereas above that temperature the ductility rapidly increases. Fig. half dozen.43 (Boone, 1977) shows the variation of ductility of several overlay coatings as a function of temperature. The ductility is measured equally strain to initiate bully of the blanket in tensile and frequently in bend tests. The transition from high-temperature ductile to lower temperature brittle behavior below the DBTT is very clear. The blanket procedure, phase distribution, composition, rut treatment history, and microstructure are some of the factors influencing the DBTT. Diffusion aluminides with predominantly β phase, which is inherently brittle, showroom college DBTT (Fig. 6.44) (Meetham, 1986) than do overlay coatings, which take microstructures containing both β and the ductile γ phases. DBTT is related to the capability of the phases to plastically deform under load.

Figure 6.43. Temperature dependence of ductility of various MCrAlY coatings.

From Boone, D.H., 1977. Airco Temescal Data Sheets. Airco Inc., Berkeley, California, U.s.a.. Courtesy of Donald H. Boone.

Figure 6.44. Ductile-to-brittle transition temperature of CoCrAlY coatings compared with diffusion aluminide.

From Meetham, Thousand.West., 1986. Employ of protective coatings in aero gas turbine engines. Mater. Sci. Technol. two, 290–294. Reprinted with permission from Maney Publishing.

The strain these coatings experience in applications such as in GTEs is imposed past the operating conditions. In such uses, the ductile-to-brittle transition behavior represented at the imposed strains helps in the selection of coatings, too equally their thickness for the structural awarding.

The effect of composition on DBTT of aluminides is very articulate from the work of Goward (1970, 1976), who determined that the DBTT of NiAl is reduced by more 100°C (180°F) when aluminum content is lowered from 32 to 25   wt%. Cobalt aluminide (CoAl) formed by aluminiding cobalt-based superalloys exhibits a DBTT somewhat college than that of nickel aluminide (NiAl) (Boone, 1976). In addition, platinum aluminide coating on nickel base superalloys IN 100 and IN 738LC exhibits higher DBTT than that of obviously aluminides because of the formation of a brittle PtAl₂ stage near the surface (Lowrie, 1952). Estimated DBTT values (Strang and Lang, 1982) of some of the aluminides are given in Table half dozen.nine.

Table 6.ix. Approximate Values of Ductile-to-Brittle Transition Temperature (DBTT) of Aluminides and MCrAlYs

Coating	Estimated DBTT, °C (°F)
NiAl	868–1060 (1594–1940)
(Ni,Pt)Al	> plain aluminide
CoAl	878–1070 (1612–1958)
Co18Cr9Al1Y	150–200 (302–392)
Co18Cr11Al1Y	250–300 (482–572)
Co20Cr12.5Al1Y	600–650 (1112–1202)
Co29Cr6Al1Y	700–800 (1292–1272)
Co27Cr12AlY	800–900 (1272–1652)
Ni20Cr9–11AlY	25–200 (77–392)
Ni38Cr11AlY	600–650 (1112–1202)
PtAlii	870–1070 (1598–1958)
Commercial platinum aluminide (temperature at which fractures at 3% strain)	∼930 (1706)

DBTT also depends somewhat on the substrate on which the coating is deposited. Coating thickness is also known to have an effect (Nicholl and Hildebrandt, 1979) on the measured DBTT.

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Fundamental Theories and Mechanisms of Failure

A. Pineau , T. Pardoen , in Comprehensive Structural Integrity, 2007

2.06.4.2.three.(i) Stress profiles alee of a growing crack

The starting bespeak for any analysis of the brittle-to-ductile transition is to rely on a audio model for ductile tearing. These models accept been presented in details in Section 2.06.3.7. Just the points specific to the understanding of the conditions leading to the transition into cleavage fracture are elaborated here. Equally explained in Section 2.06.3.vii.1, the theoretical work by Rice and Sorensen (1978) has shown that, under SSY weather and for an elastic–perfectly plastic nondamaging material, the main departure in the stress–strain field between a stationary and a growing fissure lies in the strain singularity and not the stress profile at the crevice tip. The Prandtl slip-line field is idea to employ also to a propagating crevice while the strain singularity is much lower, that is, varying as ln(r), than that corresponding to the HRR field for a stationary fissure. The normal stress ahead of the fissure tip remains shut to 3 times the yield strength of the elastic–perfectly plastic material with a yield forcefulness σ₀. These theoretical results apply to a crack which does not give rise to blunting effect. This assumption is far from reality. As already shown in Figure 71 , the crack tip is blunted at crevice initiation while during propagation the unzipping process from one inclusion to another one gives rise to a cleft-tip profile which is much sharper.

The detailed simulations past Xia and Shih (1995a, 1995b, 1996), already discussed in Department 2.06.three.7.3, take shown that, during DCG, the maximum tensile stress, σ₂₂, ahead of a simulated propagating crack, increases with fissure extension, as shown in Figure 93 . These results were obtained from numerical simulations of three-betoken bend specimens (W  =   50   mm) in a given material; for example, the ratio between Young's modulus and yield strength is equal to 500 and the work-hardening exponent is equal to 0.1. The mesh size, D, was equal to 300   μm, and ductile impairment was simulated using the version of the Gurson potential enhanced by Tvergaard and Needleman (see Section ii.06.3.iv). Three crevice depths corresponding to a/Westward  =   0.10, 0.25, and 0.60 were simulated. In this bend specimen geometry, the constraint effect is largely dependent on the crack depth. Figure 93 shows that at the early phase of fissure growth, Δa  = D, the maximum tensile stress for a/W  =   0.25 is lower than that for a/West  =   0.60. When the stress level for a/Due west  =   0.25 is followed for increasing crack lengths, it is observed that σ₂₂ increases quickly with crack growth, and at Δa  =   20D  =   half dozen   mm, the summit stress has reached the level for a/Westward  =   0.lx.   A similar consequence is observed for a/Due west  =   0.1 although the result is less pronounced. This steady elevation of crack-tip constraint with ductile crevice extension can and so increment the take chances of cleavage fracture.

Effigy 93. a, Distribution of tensile stress σ₂₂ ahead of a propagation crack for Δa  = D, Δa  =   10D, and Δa  =   xxD and for three different ratios, a/Westward, of initial crack length to specimen width; b, DCG resistance curves for three different a/W ratios in three-indicate curve specimen, with West  =   l   mm; Eastward/σ₀  =   500, north  =   0.10, five  =   0.3; D  =   200   \rmum. Source: Xia, L. and Shih, C. F. 1995a. Ductile crack growth. I: A numerical study using computational cells with microstructurally based length scales. J. Mech. Phys. Solids 43, 233–259. Xia, L. and Shih, C. F. 1995b. Ductile crack growth – 2. Void nucleation and geometry effects on macroscopic fracture behavior. J. Mech. Phys. Solids 43, 1953–1981. Xia, L. and Shih, C. F. 1996. Ductile cleft growth. III: Transition to cleavage fracture incorporating statistics. J. Mech. Phys. Solids 44, 603–639.

This effect of the stress height during crack growth is likely less pronounced in specimen geometries in which the constraint is less dependent on the scissure length, such as tensile specimens with 1 single border fissure, equally shown by Xia and Cheng (1997). For further discussion on the result of a growing crack on stress profiles at crevice tip, see too Dodds et al. (1997), Tanguy (2001), and Tanguy et al. (2002a, 2002b). It appears therefore that the DBT behavior will exist strongly dependent on the specimen geometry. Cleavage fracture will be favored in bend specimens in which the initial fissure size is relatively pocket-size. This is the situation which will exist illustrated subsequently in the analyses of Charpy V-notch specimens.

The introduction of damage alee of the crack tip produces a reduction of the 'local' stresses, when using for example the GTN model (come across Section two.06.iv.3.2) to simulate DCG. This softening outcome and its consequence on the calculation of the probability to cleavage fracture has been quantified by Busso et al. (1998). However this reduction of the 'local' stress is macroscopic. At metallurgical scales much smaller than the prison cell size, D, formation and growth of the macroscopic cell voids driving ductile cleft extension probable alter and amplify the local stress fields interim on the smaller particles that can trigger and control cleavage fracture. This local stress amplification has been studied recently by Petti and Dodds (2005b). These authors used a very simplified model consisting in cylindrical inclusions parallel to the fissure front and extending over all the specimen thickness. The result of local stress intensification due to the presence of ductile cavities has been evidenced experimentally past a number of authors; see, for case, Carassou (1999) and Carassou et al. (1998). These authors showed that, under given circumstances, cleavage cracks in A508 RPV steel were initiated from small carbide particles located effectually cavities initiated from larger inclusions. This effect of stress intensification on cleavage fracture will be more pronounced at low temperature and in materials containing a pregnant amount of large inclusions when cleavage is controlled by the nucleation of microcracks from particles. This influence of ductile damage on cleavage fracture appears therefore opposite to the softening consequence described earlier. Only detailed metallographical observations on the position and the nature of the cleavage initiating sites can be used to differentiate these 2 conflicting effects of local ductile damage on the DBT beliefs.

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Field and Faux Field Experience

Sudhangshu Bose , in Loftier Temperature Coatings (2nd Edition), 2018

Coating Cracking in Industrial Gas Turbine Engines

Local transient strains tend to crack coatings at temperatures beneath the DBTT. Such slap-up has been found to be more than prevalent in IGTs (Conner and Connor, 1994) than in aircraft engines likewise every bit laboratory rig testing. Fig. 10.5A shows bang-up in a platinum aluminide coating after 12,000   h of service in General Electric–built big IGTs. The cracks have penetrated the coating–alloy diffusion zone, which has started to exhibit signs of oxidation. An underlayer of LPPS-deposited MCrAlY coating with an aluminide overlayer (Fig. ten.5B) seems to provide a solution to keen of the blanket. The cracks notwithstanding appear in the aluminide layer but do not penetrate the overlay. The overlay coating appears to edgeless the cracks so that they do not propagate into the substrate even after 12,000   h in the same engine as shown in Fig. 10.5A. 1 possible reason for the crack blunting behavior of the overlay coating is the presence of the ductile γ phase, which can undergo plastic deformation, unlike the brittle β phase.

Effigy 10.5. (A) Cracking in platinum aluminide–coated turbine blade after 12,000   h of service in big industrial gas turbine. Cracks take penetrated the diffusion zone of the substrate that exhibits signs of onset of oxidation; (B) crack arrested at the MCrAlY–aluminide interface later 12,000   h in the same engine.

From Conner, J.A., Conner, W.B., Dec 1994. Ranking protective coatings: laboratory versus field experience. JOM, 35–38. Reprinted with permission from The Minerals, Metals & Materials Society.

The cracking resistance of the overlay coatings of γ  + β microstructure relative to the predominantly β stage of aluminides is also demonstrated in the field in other IGT engines. For example, turbine blades (buckets) of nickel base superalloys GTD 111 and IN-738 coated with platinum aluminide (22.one% aluminum in the outer layer), overaluminided CoCrAlY (16.1% aluminum in the outer layer), CoCrAlY (six.6% aluminum), and CoNiCrAlY (ten.5% aluminum) were field exposed (Yoshioka et al., 2006) for up to 38,171   h in frame 7E and 9E IGT engines. Although the oxidation capability of the coatings correlated with aluminum content, the severity of coating cracking was in the following lodge: Pt aluminide   >   overaluminided CoCrAlY   >   CoCrAlY   >   CoNiCrAlY. Detailed posttest label showed that DBTT too as minimum strain to cracking measured at elevated temperature correlated well with the not bad propensity, with cracks penetrating the alloys in the case of both platinum aluminide and overaluminided CoCrAlY. We know that for the same course of coating, the DBTT generally correlated with aluminum content, college aluminum having higher DBTT.

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Interfacial and Nanoscale Fracture

W. Gerberich , ... Due west.Yard. Mook , in Comprehensive Structural Integrity, 2003

8.10.two.4.2 Crack-tip dislocation emission

Emission criteria arose out of an experimental need to explicate the BDT and later out of a more theoretical nature to resolve the Rice paradox. While many continuum-type models existed for the BDT in the 1950s and 1960s, information technology was not until Kelly et al. (1967) considered spontaneous shear or cleavage at a crack tip that dislocation interactions were seriously considered. This was followed afterwards by the seminal Rice–Thomson (Rice and Thomson, 1974) paper which gave the BDT in terms of a core cutoff criteria. This is nicely described by Ohr (1987) and Hirsch (1995), but a cursory clarification here should suffice.

As an example, consider a typical sparse flick delamination where G might exist 0.8   J   chiliad⁻ⁱⁱ representing a K _III of 0.4   MPa   m^i/2 for a 100   GPa shear modulus cloth. Note that for illustrative purposes nosotros use mode 3 hither, whereas most thin moving-picture show situations are largely modes I and 2. For a very thin film, at that place are two solutions for the equilibrium of forces. These forces are from the applied stress intensity K _Three, the image force trying to elevate the dislocation back to the free surface, μb/4πr, and the lattice friction stress, σ _f. This forcefulness balance can exist given by (Masuda-Jindo et al., 1994; Thomson, 1986)

(17) $\frac{{\mathrm{Thousand}}_3}{\sqrt{\mathrm{two}\pi r}}-\frac{\mu b}{\mathrm{four}\pi r}-{\sigma }_{\mathrm{f}}=0$

At a typical value of the friction stress of 500   MPa, there are 2 values of the equilibrium of forces where the system is at rest, i.e., $\sum F=0.$ This is illustrated in Figure vii. Hither, we run into that the positive applied shear stress, ${\sigma }_{\mathrm{ys}}^{+}$ , times the Burger'south vector, b, would drive a nucleated dislocation away from the fissure tip. Alternatively, the image forcefulness of ${\sigma }_{\mathrm{ys}}^{-}\cdot b$ would pull the dislocation toward the crack tip. Conspicuously, for r<r _o the prototype strength would attract the emitted dislocation back into the crevice. However, since there is a lattice resistance, σ _f, the practical stress from the crevice together with the prototype forcefulness must exceed the friction stress before it can glide further. This is achieved at r _c. One time the local stress exceeds σ _f, it tin spontaneously glide from r _c to c _⊥ before it arrests. Information technology is seen that at c _⊥ the cyberspace shear stress can no longer provide a force to exceed lattice friction. For a single dislocation emitted under increasing applied stress intensity of this example, the dislocation could freely travel from the core cutoff at 0.168   nm where it exceeds r _c to the DFZ at r=94   nm=c _⊥. For the second dislocation emitted, there would exist the unproblematic equilibrium of Equation (17) plus the interactive force of the previous dislocation as already suggested by Equations (15) and (16) for shielding dislocations. The added complexity of dislocation–dislocation interactions (Atkinson and Clements, 1973) volition be illustrated in a couple of examples for external and tip sources in Section eight.x.iii.3.

Figure 7. Representation of crack-tip emission and arrest as a residue between the applied Yard _I stress field, the free surface image forcefulness, and the friction stress of Equation (17).

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Micromechanical Modelling of Rate and Temperature Dependent Fracture of Glassy Polymers

R. Estevez , ... E. Van der giessen , in European Structural Integrity Society, 2003

INTRODUCTION

The evolution of the toughness of glassy polymers with increasing loading rate shows a ductile to brittle transition followed by a 2nd transition from brittle to ductile at sufficiently high loading rates. On the basis of the ascertainment that failure of amorphous polymers in the glassy state occurs past the competition between shear yielding and crazing, it has been shown in [1] that the fourth dimension scales involved in each machinery primarily govern this competition. For loading rates where isothermal conditions prevail, the showtime transition from ductile to brittle results from this competition. The second transition from brittle to ductile is accompanied by a temperature ascent at the propagating crack tip of about hundreds of Kelvins [2] with traces of cloth decomposition on the fracture surface. Since shear yielding is a viscoplastic process and crazing involves also some viscoplasticity [3], albeit at a smaller length calibration, part of the second transition from brittle to ductile is thought to result in enhanced plastic dissipation caused by the temperature increase. For instance, Williams and Hodgkinson [4] suggested that the temperature increase promotes extensive plasticity at the crevice tip resulting in the increase of the toughness. Localized plasticity within a strip zone along the propagating crack was also invoked past Fuller et al. [2] to interpret the toughness increase with increasing loading charge per unit.

A previous written report [1] used a pocket-size-calibration yielding analysis featuring a viscoplastic model for shear yielding and a cohesive surface model for crazing to explore the start ductile to brittle transition. Whereas the above-referenced work was restricted to isothermal conditions, the present thermo-mechanical investigation incorporates the dissipation related to viscoplasticity in the bulk material as well every bit that involved in the crazing process. The idea is that the resulting local temperature rise affects their competition responses via the temperature dependence of both plasticity and crazing. Therefore, the aim of the present numerical written report is to gain insight into the key features involved in the second transition from brittle to ductile with increasing loading rate.

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The Furnishings of Helium in Irradiated Structural Alloys☆

Y. Dai , ... T. Yamamoto , in Comprehensive Nuclear Materials (Second Edition), 2020

i.07.iv.ii.two Helium furnishings on fracture backdrop and He-induced embrittlement effects

The effects of He on fast fracture, typically characterized by shifts in the DBTT measured in CVN bear on tests (ΔT), has long been a subject of significant controversy. This controversy has been fueled by studies that were interpreted to suggest that even pocket-sized to moderate amounts of He event in increases in DBTT. ^{14,34,254–256} Notwithstanding, it has been shown that at temperatures beneath about 400°C embrittlement is primarily due to irradiation hardening (Δσ _y), resulting from fine-calibration irradiation-induced dislocation obstacles. ^xx,21 The simplest relation is hardening–shift relation, which is given by

(18) $\Delta T=C\Delta {\sigma }_{\mathrm{y}}$

Here C depends on a number of variables but for irradiated FMS has an boilerplate value of ≈0.4°C MPa⁻¹ for subsized CVN tests. Thus, it is obvious that He would contribute to embrittlement of FMS to the extent that it contributes to hardening. However, as noted previously, He effects on hardening are minimal upwardly to levels of near 500 appm. Farther, almost of the information on He effects on embrittlement are confounded by the experimental techniques, like Ni and B doping, or employ of atypical fracture test methods. Irradiation embrittlement can too be induced past nonhardening mechanisms associated with changes in the local fracture properties that are controlled by coarse-scale microstructural features, like breakable trigger particles for cleavage, and segregation of elements that weaken GBs. ^20,21

The beginning data that clearly indicated a nonhardening role of He were generated in the early on STIP experiments, showing a transition from ductile and cleavage fracture modes to extremely brittle IG fracture ^xx,234 and somewhat larger than expected ΔT. Analyzes of a big database on irradiation hardening and embrittlement, including the STIP data, ²⁰ showed that He does not produce meaning nonhardening embrittlement at less than about 500 appm. Still, to a higher place this crude threshold the hardening-shift coefficient C (=ΔT/Δσ _y) increases due to weakening of the GBs associated with He accumulation, to the bespeak where they became the preferred fracture path. The database was used to derive a simple semiempirical model for CVN ΔT for 300°C irradiations every bit

(19) $C=0.4+7\times {\mathrm{x}}^{-4}\left({\mathrm{Ten}}_{\mathrm{He}}-500\right)\left(°\mathrm{C}{\mathrm{MPa}}^{-\mathrm{one}}\right)$

Equally shown in Fig. 34 the model prediction (dashed curve) ²⁵⁷ is remarkably consequent with SPNI and neutron information including more recent results. The STIP data are based on subsized CVN tests (KLST and one/3 CVN) on different FMS irradiated in STIP-I–3 up to virtually 17 dpa at temperatures below 300°C. ^xix The solid symbols are pocket-sized punch test data converted to CVN ΔT. The neutron data were taken from the literature, ^{xiv,254–259} and these results are also consistent with the assay of a larger database. ²⁰

Fig. 34. DBTT shift equally a function of irradiation dose for different FMS irradiated in STIP. Neutron-irradiation information are included for comparing.

Reproduced from Dai, Y., Wagner, Due west., 2009. J. Nucl. Mater. 389, 288. The dashed curve is drawn according to the model prediction (Eq. (19)).

As schematically illustrated in Fig. 35, the synergistic low-temperature hardening–helium embrittlement (LTHE) He threshold tin be rationalized as follows. Cleavage fracture occurs when the stress concentrated at the tip of a blunting fissure, Mσ _y, exceeds a critical local stress, ${\sigma }_c^{*}$ , over a critical book needed to actuate a brittle trigger particle. ²¹ Here, M is a stress concentration factor. Also, brittle IG fracture occurs when the crack tip stress exceeds the critical local stress ${\sigma }_{\mathrm{ig}}^{*}$ over a sufficient book needed to crack GBs. The ${\sigma }_{\mathrm{ig}}^{*}$ is initially higher than ${\sigma }_c^{*}$ ; thus, fracture occurs by transgranular cleavage (Fig. 35(a)). However, ${\sigma }_{\mathrm{ig}}^{*}$ decreases with increasing He GB accumulation, and beyond a bulk threshold level, ca. 500 appm, ${\sigma }_{\mathrm{ig}}^{*}$ falls below ${\sigma }_c^{*}$ (Fig. 35(b)). Thus, the grain boundary becomes the favored fissure path. The ${\sigma }_{\mathrm{ig}}^{*}$ continues to decrease with increasing He accumulation, resulting in an increasing increase of ΔT, even in the absenteeism of additional hardening. The transition to IG crack paths is marked by a larger fraction of grain boundary facets on the fracture surface. Note that the continued increment in Δσ _ys with higher He was non recognized at the time that this simple model was developed, thus the new insight and expanded database volition be used to refine the model.

Fig. 35. A sketch showing the mechanisms for irradiation-induced hardening (increase of yield stress, Δσ _y) and helium-induced grain boundary weakening effects (decrease in the intergranular fracture stress, ${\sigma }_{\mathrm{ig}}^{*}$ ) that elevate the brittle to ductile transition temperature.

Helium that is not clustered into bubbles is probable the most dissentious condition, with a monolayer coverage producing essentially complete grain boundary decohesion. The actual corporeality and distribution of helium on GBs has not been established and is a role of the temperature and microstructure as well as bulk X _He. Nonetheless, even at 400°C boundary bubbling are less than 1 nm in diameter. Assuming that grain purlieus helium derives from regions in the adjoining matrix and is located in spherical bubbling with equal numbers of one thousand _He atoms and vacancies, the fractional grain boundary coverage can be estimated every bit f _He = t _He X _He/[10^−iv thousand _He]; hither, t _He is the thickness (µm) of the layers that feed helium to the grain purlieus. Thus for example, f _He ≈ 0.25, assuming t _He = 0.25 µm and m _He = 5 and X _He = 500 appm. Note that this t _He may be too large considering that denuded zones are not obviously observed at GBs in STIP samples. Withal, the data are not sufficient to reach firm conclusions, and a combination of models and machinery experiments is needed to determine the partitioning of He to GBs for various microstructures and irradiation weather condition.

Other studies ^260,261 reached similar conclusions regarding the effect of He on grain purlieus strength. Indeed, simple and direct evidence is provided by the brittle fracture stresses measured in the tensile tests cited previously, which decreased from ≈1850–1640 MPa with increasing He levels from 1250 to 2500 appm. These helium-degraded ${\sigma }_{\mathrm{ig}}^{*}$ are well below the cleavage ${\sigma }_c^{*}\approx 2000\mathrm{Mpa}$ .

Embrittlement and ΔT are about properly evaluated by fracture toughness tests that are expected to show hardening–He synergisms that are similar to those measured in CVN tests. Fig. 36 shows the estimated fracture toughness (One thousand _Jq) of various FMS later on SPNI based on 3-point bend tests on small precracked bars at test temperatures approximately equal to the irradiation temperatures. ²⁶² Notation that at high dose, K _Jq decreases to less than forty MPa √grand, shut to lower shelf fracture toughness of FMS, even at the maximum irradiation temperature of 400°C. Fig. 36 likewise shows that the K _Jq of the T91 steel irradiated at LANSCE are degraded at lower doses (upward to about 4.3 dpa) ²³⁷ than in the STIP irradiations. This may be the effect of the combination of the lower irradiation temperatures and college helium generation rates in this case. Annotation that at 25°C irradiation of T91 in STIP-I to four.3 dpa likewise resulted in depression K _Jq.

Fig. 36. Fracture toughness as a function of irradiation dose for different FMS irradiated in STIP. The temperature values indicated are for testing temperatures, which are equal to or shut to irradiation temperatures. Information bands from LANSCE SPN irradiation and HFIR neutron irradiation are shown for comparison.

Reproduced from Maloy, S.A., James, M.R., Willcutt, Chiliad., et al., 2001. J. Nucl. Mater. 296, 119. ²⁶³ Jia, X., Dai, Y., 2006. J. Nucl. Mater. 356, 105–111.

Fig. 37 shows the predicted shifts in the main curve reference temperature (ΔT ₀) at 100 MPa√one thousand for FMS F82H (similar to that for Eurofer97) neutron irradiated at temperatures from 200 to 400°C as a function of the square root of dpa. The corresponding STIP SPNI ΔT ₀ data shown in Fig. 36 are estimated by adjusting the measured K _Jc to 100 MPa√g based on the master curve shape and further taking the unirradiated T ₀ as −100°C. ²⁶⁴ These approximate, just semiquantitatively correct comparisons prove that the synergistic hardening–He mechanism also results in much larger fracture toughness ΔT ₀ when compared with neutron irradiation with low He. Most notably, the estimated ΔT ₀ for the 400°C irradiation is of the lodge 700°C.

Fig. 37. Comparing of the predicted shift in the Main Bend reference temperature, ΔT ₀, with the data shown in Fig. 36 showing the drastic embrittling effect of loftier concentrations of He.

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Ductile To Brittle Transition Temperature,

Source: https://www.sciencedirect.com/topics/materials-science/ductile-to-brittle-transition

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