29:
1057:
impurities dislocations in the material. To move this defect (plastically deforming or yielding the material), a larger stress must be applied. This thus causes a higher yield stress in the material. While many material properties depend only on the composition of the bulk material, yield strength is extremely sensitive to the materials processing as well.
1056:
There are several ways in which crystalline materials can be engineered to increase their yield strength. By altering dislocation density, impurity levels, grain size (in crystalline materials), the yield strength of the material can be fine-tuned. This occurs typically by introducing defects such as
1866:
That experimentally measured yield strength is significantly lower than the expected theoretical value can be explained by the presence of dislocations and defects in the materials. Indeed, whiskers with perfect single crystal structure and defect-free surfaces have been shown to demonstrate yield
1043:
correlates roughly linearly with tensile strength for most steels, but measurements on one material cannot be used as a scale to measure strengths on another. Hardness testing can therefore be an economical substitute for tensile testing, as well as providing local variations in yield strength due
880:
Beyond the elastic limit, permanent deformation will occur. The elastic limit is, therefore, the lowest stress point at which permanent deformation can be measured. This requires a manual load-unload procedure, and the accuracy is critically dependent on the equipment used and operator skill. For
1402:
Where the presence of a secondary phase will increase yield strength by blocking the motion of dislocations within the crystal. A line defect that, while moving through the matrix, will be forced against a small particle or precipitate of the material. Dislocations can move through this particle
2348:
When these conditions are undesirable, it is essential for suppliers to be informed to provide appropriate materials. The presence of YPE is influenced by chemical composition and mill processing methods such as skin passing or temper rolling, which temporarily eliminate YPE and improve surface
1870:
The theoretical yield strength can be estimated by considering the process of yield at the atomic level. In a perfect crystal, shearing results in the displacement of an entire plane of atoms by one interatomic separation distance, b, relative to the plane below. In order for the atoms to move,
1636:
Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. As grain size decreases, the surface area to volume ratio of the grain increases, allowing more buildup of dislocations at the grain edge. Since it requires a lot of energy to move dislocations to
2336:
Yield Point
Elongation (YPE) significantly impacts the usability of steel. In the context of tensile testing and the engineering stress-strain curve, the Yield Point is the initial stress level, below the maximum stress, at which an increase in strain occurs without an increase in stress. This
2344:
YPE can lead to issues such as coil breaks, edge breaks, fluting, stretcher strain, and reel kinks or creases, which can affect both aesthetics and flatness. Coil and edge breaks may occur during either initial or subsequent customer processing, while fluting and stretcher strain arise during
1023:
Yielded structures have a lower stiffness, leading to increased deflections and decreased buckling strength. The structure will be permanently deformed when the load is removed, and may have residual stresses. Engineering metals display strain hardening, which implies that the yield stress is
1044:
to, e.g., welding or forming operations. For critical situations, tension testing is often done to eliminate ambiguity. However, it is possible to obtain stress-strain curves from indentation-based procedures, provided certain conditions are met. These procedures are grouped under the term
1010:, reach an upper yield point before dropping rapidly to a lower yield point. The material response is linear up until the upper yield point, but the lower yield point is used in structural engineering as a conservative value. If a metal is only stressed to the upper yield point, and beyond,
1212:
the material, impurity atoms in low concentrations will occupy a lattice position directly below a dislocation, such as directly below an extra half plane defect. This relieves a tensile strain directly below the dislocation by filling that empty lattice space with the impurity atom.
2101:
1871:
considerable force must be applied to overcome the lattice energy and move the atoms in the top plane over the lower atoms and into a new lattice site. The applied stress to overcome the resistance of a perfect lattice to shear is the theoretical yield strength, τ
1467:
1094:, which increases their density in the material. This increases the yield strength of the material since now more stress must be applied to move these dislocations through a crystal lattice. Dislocations can also interact with each other, becoming entangled.
1539:
2181:
1867:
stress approaching the theoretical value. For example, nanowhiskers of copper were shown to undergo brittle fracture at 1 GPa, a value much higher than the strength of bulk copper and approaching the theoretical value.
1944:
1278:
2332:
exhibit a distinct upper yield point or a delay in work hardening. These tensile testing phenomena, wherein the strain increases but stress does not increase as expected, are two types of yield point elongation.
1032:
Yield strength testing involves taking a small sample with a fixed cross-section area and then pulling it with a controlled, gradually increasing force until the sample changes shape or breaks. This is called a
1000:
is multiplied by a factor of safety to obtain a lower value of the offset yield point. High strength steel and aluminum alloys do not exhibit a yield point, so this offset yield point is used on these materials.
1975:
1705:
1637:
another grain, these dislocations build up along the boundary, and increase the yield stress of the material. Also known as Hall-Petch strengthening, this type of strengthening is governed by the formula:
1144:
410:
2271:
1598:
1878:
The stress displacement curve of a plane of atoms varies sinusoidally as stress peaks when an atom is forced over the atom below and then falls as the atom slides into the next lattice point.
1412:
1626:
1570:
971:
938:
2315:
885:, such as rubber, the elastic limit is much larger than the proportionality limit. Also, precise strain measurements have shown that plastic strain begins at very low stresses.
998:
344:, which is the load-bearing capacity for a given material. The ratio of yield strength to ultimate tensile strength is an important parameter for applications such steel for
1969:
is the interatomic separation distance. Since τ = G γ and dτ/dγ = G at small strains (i.e. Single atomic distance displacements), this equation becomes:
2211:
302:
and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable
1738:
1174:
1392:
89:
65:
2337:
characteristic is typical of certain materials, indicating the presence of YPE. The mechanism for YPE has been related to carbon diffusion, and more specifically to
1372:
1301:
1198:
1967:
1782:
1760:
1345:
1325:
306:
in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. For most metals, such as
1478:
238:
2547:
2800:
2112:
2411:"Automated Calculation of Strain Hardening Parameters from Tensile Stress vs. Strain Data for Low Carbon Steel Exhibiting Yield Point Elongation"
1403:
either by shearing the particle or by a process known as bowing or ringing, in which a new ring of dislocations is created around the particle.
1884:
2876:
1222:
2483:
2096:{\displaystyle G={\frac {d\tau }{dx}}={\frac {2\pi }{b}}\tau _{\max }\cos \left({\frac {2\pi x}{b}}\right)={\frac {2\pi }{b}}\tau _{\max }}
907:
is arbitrarily defined. The value for this is commonly set at 0.1% or 0.2% plastic strain. The offset value is given as a subscript, e.g.,
3069:
2448:
1643:
689:
283:
is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as
860:
move. This definition is rarely used since dislocations move at very low stresses, and detecting such movement is very difficult.
1863:
The theoretical yield strength of a perfect crystal is much higher than the observed stress at the initiation of plastic flow.
231:
2578:
3060:
3027:
2991:
2957:
2935:
2914:
2627:
1103:
317:, there is a gradual onset of non-linear behavior, and no precise yield point. In such a case, the offset yield point (or
362:
284:
276:
2223:
1575:
2776:
3045:
3010:
2976:
224:
2521:
1462:{\displaystyle \Delta \tau ={\frac {r_{\text{particle}}}{l_{\text{interparticle}}}}\gamma _{\text{particle-matrix}}}
3104:
2374:
2106:
For small displacement of γ=x/a, where a is the spacing of atoms on the slip plane, this can be rewritten as:
2814:
Richter, Gunther (2009). "Ultrahigh
Strength Single-Crystalline Nanowhiskers Grown by Physical Vapor Deposition".
1603:
2349:
quality. However, YPE can return over time due to aging, which is holding at a temperature usually 200-400 °C.
2345:
forming. Reel kinks, transverse ridges on successive inner wraps of a coil, are caused by the coiling process.
3094:
3084:
2326:
3109:
2554:
1547:
1079:
1069:
891:
The point in the stress-strain curve at which the curve levels off and plastic deformation begins to occur.
299:
1074:
943:
910:
187:
2279:
177:
2379:
976:
522:
349:
341:
192:
2836:
3099:
2189:
1716:
1152:
1045:
903:
When a yield point is not easily defined on the basis of the shape of the stress-strain curve an
846:
197:
32:
20:
2487:
2831:
2357:
1377:
167:
74:
849:
exhibited by real materials. In addition, there are several possible ways to define yielding:
2619:
2613:
2384:
1037:
Longitudinal and/or transverse strain is recorded using mechanical or optical extensometers.
101:
50:
2452:
2823:
2728:
2369:
1350:
1286:
1183:
1040:
326:
272:
268:
8:
2338:
359:, the yield point can be specified in terms of the three-dimensional principal stresses (
321:) is taken as the stress at which 0.2% plastic deformation occurs. Yielding is a gradual
264:
182:
147:
2827:
2732:
1534:{\displaystyle \Delta \tau ={\frac {Gb}{l_{\text{interparticle}}-2r_{\text{particle}}}}}
870:), so the stress-strain graph is a straight line, and the gradient will be equal to the
3089:
2794:
2746:
1952:
1767:
1745:
1330:
1310:
280:
172:
152:
96:
68:
44:
2656:
3056:
3041:
3023:
3006:
2987:
2972:
2953:
2931:
2924:
Avallone, Eugene A.; Baumeister, Theodore; Sadegh, Ali; Marks, Lionel Simeon (2006).
2910:
2849:
2782:
2772:
2750:
2643:
Barnes, Howard (1999). "The yield stress—a review or 'παντα ρει'—everything flows?".
2623:
2430:
252:
142:
40:
2841:
2736:
2652:
2422:
330:
3017:
2947:
2925:
1034:
871:
588:
549:
356:
303:
2589:
A. M. Howatson, P. G. Lund and J. D. Todd, "Engineering Tables and Data", p. 41.
2426:
1177:
1176:
is the yield stress, G is the shear elastic modulus, b is the magnitude of the
1064:
867:
574:
112:
19:
This article is about the science of material yield. For predicting yield, see
2741:
2716:
2352:
Despite its drawbacks, YPE offers advantages in certain applications, such as
1011:
845:
It is often difficult to precisely define yielding due to the wide variety of
3078:
2786:
2717:"Correlation of Yield Strength and Tensile Strength with Hardness for Steels"
2525:
2434:
2410:
2389:
2176:{\displaystyle G={\frac {d\tau }{d\gamma }}={\frac {2\pi a}{b}}\tau _{\max }}
536:
413:
322:
202:
106:
2904:
2853:
2353:
1304:
509:
420:. A variety of yield criteria have been developed for different materials.
1091:
857:
640:
613:
311:
256:
1939:{\displaystyle \tau =\tau _{\max }\sin \left({\frac {2\pi x}{b}}\right)}
1007:
496:
472:
2845:
2409:
Scales, M.; Kornuta, J.A.; Switzner, N.; Veloo, P. (1 December 2023).
1273:{\displaystyle \Delta \tau =Gb{\sqrt {C_{s}}}\epsilon ^{\frac {3}{2}}}
882:
563:
447:
337:
307:
137:
3050:
830:
816:
788:
653:
345:
162:
132:
2946:
Beer, Ferdinand P.; Johnston, E. Russell; Dewolf, John T. (2001).
1394:
is the strain induced in the lattice due to adding the impurity.
774:
157:
866:
Up to this amount of stress, stress is proportional to strain (
760:
675:
671:
667:
1700:{\displaystyle \sigma _{y}=\sigma _{0}+kd^{-{\frac {1}{2}}}\,}
28:
2967:
Boresi, A. P., Schmidt, R. J., and
Sidebottom, O. M. (1993).
2923:
2329:
1209:
627:
340:
materials, the yield strength is typically distinct from the
314:
1600:
is the surface tension between the matrix and the particle,
2905:
Avallone, Eugene A. & Baumeister III, Theodore (1996).
702:
207:
2408:
2982:
Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003).
802:
2930:(11th, Illustrated ed.). McGraw-Hill Professional.
279:
and will return to its original shape when the applied
2325:
During monotonic tensile testing, some metals such as
2276:
The theoretical yield strength can be approximated as
2282:
2226:
2192:
2115:
1978:
1955:
1887:
1770:
1748:
1719:
1646:
1606:
1578:
1550:
1481:
1415:
1397:
1380:
1353:
1333:
1313:
1289:
1225:
1186:
1155:
1106:
979:
946:
913:
365:
77:
53:
2611:
1139:{\displaystyle \Delta \sigma _{y}=Gb{\sqrt {\rho }}}
3053:
Roark's
Formulas for Stress and Strain, 7th edition
3051:Young, Warren C. & Budynas, Richard G. (2002).
3001:Oberg, E., Jones, F. D., and Horton, H. L. (1984).
1060:These mechanisms for crystalline materials include
405:{\displaystyle \sigma _{1},\sigma _{2},\sigma _{3}}
2981:
2945:
2508:
2309:
2266:{\displaystyle \tau _{\max }={\frac {Gb}{2\pi a}}}
2265:
2205:
2175:
2095:
1961:
1938:
1776:
1754:
1732:
1699:
1620:
1593:{\displaystyle \gamma _{\text{particle-matrix}}\,}
1592:
1564:
1533:
1461:
1386:
1366:
1339:
1319:
1295:
1272:
1192:
1168:
1138:
1018:
992:
965:
932:
404:
83:
59:
16:Phenomenon of deformation due to structural stress
2927:Mark's Standard Handbook for Mechanical Engineers
2907:Mark's Standard Handbook for Mechanical Engineers
275:behavior. Below the yield point, a material will
3076:
2721:Journal of Materials Engineering and Performance
2360:. Generally, steel with YPE is highly formable.
2288:
2232:
2198:
2168:
2088:
2028:
1899:
2714:
2320:
1631:
1203:
348:, and has been found to be proportional to the
2877:"Yield Point Elongation (YPE) – Pros and Cons"
1024:increased after unloading from a yield state.
1788:
1097:The governing formula for this mechanism is:
232:
2799:: CS1 maint: multiple names: authors list (
2618:. Boston: Houghton Mifflin Company. p.
2615:Engineering Materials and their Applications
1740:is the stress required to move dislocations,
1216:The relationship of this mechanism goes as:
1090:Where deforming the material will introduce
3036:Shigley, J. E., and Mischke, C. R. (1989).
2612:Flinn, Richard A.; Trojan, Paul K. (1975).
1051:
2762:
2760:
1621:{\displaystyle l_{\text{interparticle}}\,}
973:MPa. For most practical engineering uses,
239:
225:
2835:
2740:
2680:
2678:
1696:
1617:
1589:
1561:
2984:Materials and Processes in Manufacturing
2645:Journal of Non-Newtonian Fluid Mechanics
2636:
27:
2909:(8th ed.). New York: McGraw-Hill.
2813:
2757:
1628:is the distance between the particles.
3077:
2715:Pavlina, E.J.; Van Tyne, C.J. (2008).
2675:
2642:
2592:
2522:"Technical Product Data Sheets UHMWPE"
1347:are the same as in the above example,
2971:, 5th edition John Wiley & Sons.
2871:
2869:
2867:
2865:
2863:
1565:{\displaystyle r_{\text{particle}}\,}
438:
433:
3015:
2684:
2669:
1374:is the concentration of solute and
966:{\displaystyle R_{\text{p0.2}}=350}
933:{\displaystyle R_{\text{p0.1}}=310}
616:10% Ni, 1.6% Fe, 1% Mn, balance Cu
13:
3005:, 22nd edition. Industrial Press.
2860:
2766:
2310:{\displaystyle \tau _{\max }=G/30}
1802:Experimental shear strength (GPa)
1482:
1416:
1398:Particle/precipitate strengthening
1226:
1107:
14:
3121:
1799:Theoretical shear strength (GPa)
1085:
2769:Mechanical behavior of materials
2509:Beer, Johnston & Dewolf 2001
2375:Specified minimum yield strength
1472:and the bowing/ringing formula:
471:Steel, high strength alloy ASTM
2969:Advanced Mechanics of Materials
2898:
2807:
2708:
2699:
2690:
2663:
2605:
1307:, related to the yield stress,
1019:Usage in structural engineering
993:{\displaystyle R_{\text{p0.2}}}
2583:
2572:
2540:
2514:
2502:
2476:
2467:
2441:
2402:
1406:The shearing formula goes as:
877:Elastic limit (yield strength)
423:
271:behavior and the beginning of
1:
3038:Mechanical Engineering Design
2952:(3rd ed.). McGraw-Hill.
2881:www.baileymetalprocessing.com
2767:H., Courtney, Thomas (2005).
2657:10.1016/S0377-0257(98)00094-9
2395:
2206:{\displaystyle \tau _{\max }}
3040:, 5th edition. McGraw Hill.
3022:. City: Albion/Horwood Pub.
2321:Yield point elongation (YPE)
1632:Grain boundary strengthening
1204:Solid solution strengthening
1200:is the dislocation density.
1080:Grain boundary strengthening
1070:Solid solution strengthening
1003:Upper and lower yield points
485:Steel, prestressing strands
267:that indicates the limit of
7:
2363:
1762:is a material constant, and
1733:{\displaystyle \sigma _{0}}
1169:{\displaystyle \sigma _{y}}
1075:Precipitation strengthening
856:The lowest stress at which
427:
188:Metal-induced embrittlement
10:
3126:
2427:10.1007/s40799-023-00626-4
1789:Theoretical yield strength
1027:
178:Liquid metal embrittlement
18:
3055:. New York: McGraw-Hill.
2742:10.1007/s11665-008-9225-5
2380:Ultimate tensile strength
1387:{\displaystyle \epsilon }
523:High-density polyethylene
350:strain hardening exponent
342:ultimate tensile strength
193:Stress corrosion cracking
84:{\displaystyle \epsilon }
67:, shown as a function of
1572:is the particle radius,
1052:Strengthening mechanisms
125:Mechanical failure modes
3105:Deformation (mechanics)
2986:(9th ed.). Wiley.
2548:"unitex-deutschland.eu"
2415:Experimental Techniques
1046:Indentation plastometry
552:AISI 302 – cold-rolled
198:Sulfide stress cracking
60:{\displaystyle \sigma }
21:Material failure theory
2949:Mechanics of Materials
2311:
2267:
2207:
2177:
2097:
1963:
1940:
1778:
1756:
1734:
1701:
1622:
1594:
1566:
1535:
1463:
1388:
1368:
1341:
1321:
1297:
1274:
1194:
1170:
1140:
994:
967:
934:
406:
325:which is normally not
168:Hydrogen embrittlement
119:
85:
61:
2600:Mechanical Metallurgy
2385:Yield curve (physics)
2312:
2268:
2208:
2178:
2098:
1964:
1941:
1779:
1757:
1735:
1702:
1623:
1595:
1567:
1536:
1464:
1389:
1369:
1367:{\displaystyle C_{s}}
1342:
1322:
1298:
1296:{\displaystyle \tau }
1275:
1195:
1193:{\displaystyle \rho }
1171:
1141:
1006:Some metals, such as
995:
968:
935:
863:Proportionality limit
407:
102:Proportionality limit
91:):
86:
62:
31:
3095:Plasticity (physics)
3085:Elasticity (physics)
3003:Machinery's Handbook
2370:Plasticity (physics)
2339:Cottrell atmospheres
2280:
2224:
2190:
2113:
1976:
1953:
1885:
1768:
1746:
1717:
1644:
1604:
1576:
1548:
1479:
1413:
1378:
1351:
1331:
1311:
1287:
1223:
1184:
1153:
1104:
1041:Indentation hardness
977:
944:
911:
894:Offset yield point (
847:stress–strain curves
727:Aluminium (annealed)
363:
75:
51:
3110:Structural analysis
3070:Engineer's Handbook
3019:Mechanics of Solids
2828:2009NanoL...9.3048R
2733:2008JMEP...17..888P
2602:, McGraw-Hill, 1986
1544:In these formulas,
285:plastic deformation
265:stress-strain curve
183:Mechanical overload
33:Stress–strain curve
2771:. Waveland Press.
2528:on 14 October 2011
2473:ASTM A228-A228M-14
2307:
2263:
2203:
2186:Giving a value of
2173:
2093:
1959:
1936:
1784:is the grain size.
1774:
1752:
1730:
1697:
1618:
1590:
1562:
1531:
1459:
1384:
1364:
1337:
1317:
1293:
1270:
1190:
1166:
1136:
990:
963:
930:
905:offset yield point
853:True elastic limit
566:4.5% C, ASTM A-48
460:Steel, API 5L X65
402:
277:deform elastically
263:is the point on a
120:
97:True elastic limit
81:
57:
3062:978-0-07-072542-3
3029:978-1-898563-67-9
3016:Ross, C. (1999).
2993:978-0-471-65653-1
2959:978-0-07-365935-0
2937:978-0-07-142867-5
2916:978-0-07-004997-0
2846:10.1021/nl9015107
2629:978-0-395-18916-0
2261:
2161:
2140:
2081:
2059:
2021:
2003:
1962:{\displaystyle b}
1930:
1861:
1860:
1777:{\displaystyle d}
1755:{\displaystyle k}
1692:
1614:
1586:
1558:
1529:
1525:
1509:
1456:
1447:
1444:
1434:
1340:{\displaystyle b}
1320:{\displaystyle G}
1267:
1253:
1134:
987:
954:
921:
843:
842:
738:Copper (annealed)
439:Ultimate strength
300:material property
253:materials science
249:
248:
143:Corrosion fatigue
41:nonferrous alloys
3117:
3066:
3033:
2997:
2963:
2941:
2920:
2892:
2891:
2889:
2887:
2873:
2858:
2857:
2839:
2822:(8): 3048–3052.
2811:
2805:
2804:
2798:
2790:
2764:
2755:
2754:
2744:
2712:
2706:
2705:Degarmo, p. 377.
2703:
2697:
2694:
2688:
2682:
2673:
2667:
2661:
2660:
2651:(1–2): 133–178.
2640:
2634:
2633:
2609:
2603:
2596:
2590:
2587:
2581:
2576:
2570:
2569:
2567:
2565:
2560:on 25 March 2012
2559:
2553:. Archived from
2552:
2544:
2538:
2537:
2535:
2533:
2524:. Archived from
2518:
2512:
2506:
2500:
2499:
2497:
2495:
2486:. Archived from
2480:
2474:
2471:
2465:
2464:
2462:
2460:
2451:. Archived from
2445:
2439:
2438:
2421:(6): 1311–1322.
2406:
2316:
2314:
2313:
2308:
2303:
2292:
2291:
2272:
2270:
2269:
2264:
2262:
2260:
2249:
2241:
2236:
2235:
2212:
2210:
2209:
2204:
2202:
2201:
2182:
2180:
2179:
2174:
2172:
2171:
2162:
2157:
2146:
2141:
2139:
2131:
2123:
2102:
2100:
2099:
2094:
2092:
2091:
2082:
2077:
2069:
2064:
2060:
2055:
2044:
2032:
2031:
2022:
2017:
2009:
2004:
2002:
1994:
1986:
1968:
1966:
1965:
1960:
1945:
1943:
1942:
1937:
1935:
1931:
1926:
1915:
1903:
1902:
1793:
1792:
1783:
1781:
1780:
1775:
1761:
1759:
1758:
1753:
1739:
1737:
1736:
1731:
1729:
1728:
1706:
1704:
1703:
1698:
1695:
1694:
1693:
1685:
1669:
1668:
1656:
1655:
1627:
1625:
1624:
1619:
1616:
1615:
1612:
1599:
1597:
1596:
1591:
1588:
1587:
1584:
1571:
1569:
1568:
1563:
1560:
1559:
1556:
1540:
1538:
1537:
1532:
1530:
1528:
1527:
1526:
1523:
1511:
1510:
1507:
1500:
1492:
1468:
1466:
1465:
1460:
1458:
1457:
1454:
1448:
1446:
1445:
1442:
1436:
1435:
1432:
1426:
1393:
1391:
1390:
1385:
1373:
1371:
1370:
1365:
1363:
1362:
1346:
1344:
1343:
1338:
1326:
1324:
1323:
1318:
1302:
1300:
1299:
1294:
1279:
1277:
1276:
1271:
1269:
1268:
1260:
1254:
1252:
1251:
1242:
1199:
1197:
1196:
1191:
1175:
1173:
1172:
1167:
1165:
1164:
1145:
1143:
1142:
1137:
1135:
1130:
1119:
1118:
999:
997:
996:
991:
989:
988:
985:
972:
970:
969:
964:
956:
955:
952:
939:
937:
936:
931:
923:
922:
919:
899:
898:
874:of the material.
716:Nylon, type 6/6
602:Copper 99.9% Cu
428:
411:
409:
408:
403:
401:
400:
388:
387:
375:
374:
331:ultimate failure
241:
234:
227:
122:
121:
90:
88:
87:
82:
66:
64:
63:
58:
35:showing typical
3125:
3124:
3120:
3119:
3118:
3116:
3115:
3114:
3100:Solid mechanics
3075:
3074:
3063:
3030:
2994:
2960:
2938:
2917:
2901:
2896:
2895:
2885:
2883:
2875:
2874:
2861:
2837:10.1.1.702.1801
2812:
2808:
2792:
2791:
2779:
2765:
2758:
2713:
2709:
2704:
2700:
2696:ISO 6892-1:2009
2695:
2691:
2683:
2676:
2668:
2664:
2641:
2637:
2630:
2610:
2606:
2597:
2593:
2588:
2584:
2577:
2573:
2563:
2561:
2557:
2550:
2546:
2545:
2541:
2531:
2529:
2520:
2519:
2515:
2507:
2503:
2493:
2491:
2490:on 19 July 2011
2482:
2481:
2477:
2472:
2468:
2458:
2456:
2455:on 22 June 2012
2447:
2446:
2442:
2407:
2403:
2398:
2366:
2323:
2299:
2287:
2283:
2281:
2278:
2277:
2250:
2242:
2240:
2231:
2227:
2225:
2222:
2221:
2216:
2197:
2193:
2191:
2188:
2187:
2167:
2163:
2147:
2145:
2132:
2124:
2122:
2114:
2111:
2110:
2087:
2083:
2070:
2068:
2045:
2043:
2039:
2027:
2023:
2010:
2008:
1995:
1987:
1985:
1977:
1974:
1973:
1954:
1951:
1950:
1916:
1914:
1910:
1898:
1894:
1886:
1883:
1882:
1874:
1791:
1769:
1766:
1765:
1747:
1744:
1743:
1724:
1720:
1718:
1715:
1714:
1684:
1680:
1676:
1664:
1660:
1651:
1647:
1645:
1642:
1641:
1634:
1611:
1607:
1605:
1602:
1601:
1585:particle-matrix
1583:
1579:
1577:
1574:
1573:
1555:
1551:
1549:
1546:
1545:
1522:
1518:
1506:
1502:
1501:
1493:
1491:
1480:
1477:
1476:
1455:particle-matrix
1453:
1449:
1441:
1437:
1431:
1427:
1425:
1414:
1411:
1410:
1400:
1379:
1376:
1375:
1358:
1354:
1352:
1349:
1348:
1332:
1329:
1328:
1312:
1309:
1308:
1288:
1285:
1284:
1259:
1255:
1247:
1243:
1241:
1224:
1221:
1220:
1206:
1185:
1182:
1181:
1160:
1156:
1154:
1151:
1150:
1129:
1114:
1110:
1105:
1102:
1101:
1088:
1054:
1030:
1021:
984:
980:
978:
975:
974:
951:
947:
945:
942:
941:
918:
914:
912:
909:
908:
896:
895:
872:elastic modulus
749:Iron (annealed)
589:Aluminium alloy
550:Stainless steel
440:
435:
426:
418:yield criterion
396:
392:
383:
379:
370:
366:
364:
361:
360:
357:solid mechanics
245:
118:
117:
76:
73:
72:
52:
49:
48:
24:
17:
12:
11:
5:
3123:
3113:
3112:
3107:
3102:
3097:
3092:
3087:
3073:
3072:
3067:
3061:
3048:
3034:
3028:
3013:
2999:
2992:
2979:
2965:
2958:
2943:
2936:
2921:
2915:
2900:
2897:
2894:
2893:
2859:
2806:
2778:978-1577664253
2777:
2756:
2727:(6): 888–893.
2707:
2698:
2689:
2674:
2662:
2635:
2628:
2604:
2591:
2582:
2571:
2539:
2513:
2511:, p. 746.
2501:
2484:"complore.com"
2475:
2466:
2440:
2400:
2399:
2397:
2394:
2393:
2392:
2387:
2382:
2377:
2372:
2365:
2362:
2356:, and reduces
2322:
2319:
2306:
2302:
2298:
2295:
2290:
2286:
2274:
2273:
2259:
2256:
2253:
2248:
2245:
2239:
2234:
2230:
2214:
2200:
2196:
2184:
2183:
2170:
2166:
2160:
2156:
2153:
2150:
2144:
2138:
2135:
2130:
2127:
2121:
2118:
2104:
2103:
2090:
2086:
2080:
2076:
2073:
2067:
2063:
2058:
2054:
2051:
2048:
2042:
2038:
2035:
2030:
2026:
2020:
2016:
2013:
2007:
2001:
1998:
1993:
1990:
1984:
1981:
1958:
1947:
1946:
1934:
1929:
1925:
1922:
1919:
1913:
1909:
1906:
1901:
1897:
1893:
1890:
1872:
1859:
1858:
1855:
1852:
1848:
1847:
1844:
1841:
1837:
1836:
1833:
1830:
1826:
1825:
1822:
1819:
1815:
1814:
1811:
1808:
1804:
1803:
1800:
1797:
1790:
1787:
1786:
1785:
1773:
1763:
1751:
1741:
1727:
1723:
1708:
1707:
1691:
1688:
1683:
1679:
1675:
1672:
1667:
1663:
1659:
1654:
1650:
1633:
1630:
1610:
1582:
1554:
1542:
1541:
1521:
1517:
1514:
1505:
1499:
1496:
1490:
1487:
1484:
1470:
1469:
1452:
1440:
1430:
1424:
1421:
1418:
1399:
1396:
1383:
1361:
1357:
1336:
1316:
1292:
1281:
1280:
1266:
1263:
1258:
1250:
1246:
1240:
1237:
1234:
1231:
1228:
1205:
1202:
1189:
1178:Burgers vector
1163:
1159:
1147:
1146:
1133:
1128:
1125:
1122:
1117:
1113:
1109:
1087:
1086:Work hardening
1084:
1083:
1082:
1077:
1072:
1067:
1065:Work hardening
1053:
1050:
1029:
1026:
1020:
1017:
1016:
1015:
1004:
1001:
983:
962:
959:
950:
929:
926:
917:
901:
892:
889:
886:
878:
875:
864:
861:
854:
841:
840:
837:
834:
827:
826:
823:
820:
813:
812:
809:
806:
799:
798:
795:
792:
785:
784:
781:
778:
771:
770:
767:
764:
757:
756:
753:
750:
746:
745:
742:
739:
735:
734:
731:
728:
724:
723:
720:
717:
713:
712:
709:
706:
699:
698:
695:
692:
686:
685:
682:
679:
664:
663:
660:
657:
650:
649:
646:
643:
637:
636:
633:
630:
624:
623:
620:
617:
610:
609:
606:
603:
599:
598:
595:
592:
585:
584:
581:
578:
577:(6% Al, 4% V)
575:Titanium alloy
571:
570:
567:
560:
559:
556:
553:
546:
545:
542:
539:
533:
532:
529:
526:
519:
518:
515:
513:
506:
505:
502:
499:
493:
492:
489:
486:
482:
481:
478:
475:
468:
467:
464:
461:
457:
456:
453:
450:
443:
442:
437:
434:Yield strength
432:
425:
422:
399:
395:
391:
386:
382:
378:
373:
369:
292:yield strength
247:
246:
244:
243:
236:
229:
221:
218:
217:
216:
215:
210:
205:
200:
195:
190:
185:
180:
175:
170:
165:
160:
155:
150:
145:
140:
135:
127:
126:
116:
115:
113:yield strength
109:
104:
99:
93:
92:
80:
56:
15:
9:
6:
4:
3:
2:
3122:
3111:
3108:
3106:
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3082:
3080:
3071:
3068:
3064:
3058:
3054:
3049:
3047:
3046:0-07-056899-5
3043:
3039:
3035:
3031:
3025:
3021:
3020:
3014:
3012:
3011:0-8311-1155-0
3008:
3004:
3000:
2995:
2989:
2985:
2980:
2978:
2977:0-471-55157-0
2974:
2970:
2966:
2961:
2955:
2951:
2950:
2944:
2939:
2933:
2929:
2928:
2922:
2918:
2912:
2908:
2903:
2902:
2882:
2878:
2872:
2870:
2868:
2866:
2864:
2855:
2851:
2847:
2843:
2838:
2833:
2829:
2825:
2821:
2817:
2810:
2802:
2796:
2788:
2784:
2780:
2774:
2770:
2763:
2761:
2752:
2748:
2743:
2738:
2734:
2730:
2726:
2722:
2718:
2711:
2702:
2693:
2687:, p. 59.
2686:
2681:
2679:
2672:, p. 56.
2671:
2666:
2658:
2654:
2650:
2646:
2639:
2631:
2625:
2621:
2617:
2616:
2608:
2601:
2595:
2586:
2580:
2575:
2556:
2549:
2543:
2527:
2523:
2517:
2510:
2505:
2489:
2485:
2479:
2470:
2454:
2450:
2449:"ussteel.com"
2444:
2436:
2432:
2428:
2424:
2420:
2416:
2412:
2405:
2401:
2391:
2390:Yield surface
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2371:
2368:
2367:
2361:
2359:
2355:
2350:
2346:
2342:
2340:
2334:
2331:
2328:
2318:
2304:
2300:
2296:
2293:
2284:
2257:
2254:
2251:
2246:
2243:
2237:
2228:
2220:
2219:
2218:
2194:
2164:
2158:
2154:
2151:
2148:
2142:
2136:
2133:
2128:
2125:
2119:
2116:
2109:
2108:
2107:
2084:
2078:
2074:
2071:
2065:
2061:
2056:
2052:
2049:
2046:
2040:
2036:
2033:
2024:
2018:
2014:
2011:
2005:
1999:
1996:
1991:
1988:
1982:
1979:
1972:
1971:
1970:
1956:
1932:
1927:
1923:
1920:
1917:
1911:
1907:
1904:
1895:
1891:
1888:
1881:
1880:
1879:
1876:
1868:
1864:
1856:
1853:
1850:
1849:
1845:
1842:
1839:
1838:
1834:
1831:
1828:
1827:
1823:
1820:
1817:
1816:
1812:
1809:
1806:
1805:
1801:
1798:
1795:
1794:
1771:
1764:
1749:
1742:
1725:
1721:
1713:
1712:
1711:
1689:
1686:
1681:
1677:
1673:
1670:
1665:
1661:
1657:
1652:
1648:
1640:
1639:
1638:
1629:
1613:interparticle
1608:
1580:
1552:
1519:
1515:
1512:
1508:interparticle
1503:
1497:
1494:
1488:
1485:
1475:
1474:
1473:
1450:
1443:interparticle
1438:
1428:
1422:
1419:
1409:
1408:
1407:
1404:
1395:
1381:
1359:
1355:
1334:
1314:
1306:
1290:
1264:
1261:
1256:
1248:
1244:
1238:
1235:
1232:
1229:
1219:
1218:
1217:
1214:
1211:
1201:
1187:
1179:
1161:
1157:
1131:
1126:
1123:
1120:
1115:
1111:
1100:
1099:
1098:
1095:
1093:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1063:
1062:
1061:
1058:
1049:
1047:
1042:
1038:
1036:
1035:tensile test.
1025:
1013:
1009:
1005:
1002:
981:
960:
957:
948:
927:
924:
915:
906:
902:
893:
890:
887:
884:
879:
876:
873:
869:
865:
862:
859:
855:
852:
851:
850:
848:
838:
835:
832:
829:
828:
824:
821:
818:
815:
814:
810:
807:
804:
801:
800:
796:
793:
790:
787:
786:
782:
779:
776:
773:
772:
768:
765:
762:
759:
758:
754:
751:
748:
747:
743:
740:
737:
736:
732:
729:
726:
725:
721:
718:
715:
714:
710:
707:
704:
701:
700:
696:
693:
691:
688:
687:
683:
680:
677:
673:
669:
666:
665:
661:
658:
655:
652:
651:
647:
644:
642:
639:
638:
634:
631:
629:
626:
625:
621:
618:
615:
612:
611:
607:
604:
601:
600:
596:
593:
590:
587:
586:
582:
579:
576:
573:
572:
568:
565:
562:
561:
557:
554:
551:
548:
547:
543:
540:
538:
537:Polypropylene
535:
534:
530:
527:
524:
521:
520:
516:
514:
511:
508:
507:
503:
500:
498:
495:
494:
490:
487:
484:
483:
479:
476:
474:
470:
469:
465:
462:
459:
458:
454:
451:
449:
445:
444:
430:
429:
421:
419:
415:
414:yield surface
397:
393:
389:
384:
380:
376:
371:
367:
358:
353:
351:
347:
343:
339:
334:
332:
328:
324:
320:
316:
313:
309:
305:
301:
297:
293:
288:
286:
282:
278:
274:
270:
266:
262:
258:
254:
242:
237:
235:
230:
228:
223:
222:
220:
219:
214:
211:
209:
206:
204:
203:Thermal shock
201:
199:
196:
194:
191:
189:
186:
184:
181:
179:
176:
174:
171:
169:
166:
164:
161:
159:
156:
154:
151:
149:
146:
144:
141:
139:
136:
134:
131:
130:
129:
128:
124:
123:
114:
110:
108:
107:Elastic limit
105:
103:
100:
98:
95:
94:
78:
70:
54:
46:
42:
39:behavior for
38:
34:
30:
26:
22:
3052:
3037:
3018:
3002:
2983:
2968:
2948:
2926:
2906:
2899:Bibliography
2884:. Retrieved
2880:
2819:
2816:Nano Letters
2815:
2809:
2768:
2724:
2720:
2710:
2701:
2692:
2665:
2648:
2644:
2638:
2614:
2607:
2599:
2594:
2585:
2574:
2562:. Retrieved
2555:the original
2542:
2530:. Retrieved
2526:the original
2516:
2504:
2494:10 September
2492:. Retrieved
2488:the original
2478:
2469:
2457:. Retrieved
2453:the original
2443:
2418:
2414:
2404:
2354:roll forming
2351:
2347:
2343:
2335:
2324:
2275:
2185:
2105:
1948:
1877:
1869:
1865:
1862:
1709:
1635:
1543:
1471:
1405:
1401:
1305:shear stress
1282:
1215:
1207:
1148:
1096:
1092:dislocations
1089:
1059:
1055:
1039:
1031:
1022:
1014:can develop.
1012:Lüders bands
904:
897:proof stress
858:dislocations
844:
510:Carbon fiber
417:
354:
335:
327:catastrophic
323:failure mode
319:proof stress
318:
296:yield stress
295:
291:
289:
260:
250:
212:
36:
25:
2598:G. Dieter,
888:Yield point
868:Hooke's law
641:Spider silk
614:Cupronickel
424:Definitions
312:cold-worked
261:yield point
257:engineering
3079:Categories
2579:matweb.com
2396:References
2358:springback
2217:equal to:
1851:α-Fe
1008:mild steel
883:elastomers
833:(annealed)
819:(annealed)
805:(annealed)
791:(annealed)
777:(annealed)
763:(annealed)
512:(CF, CFK)
504:1740–3300
497:Piano wire
3090:Mechanics
2832:CiteSeerX
2795:cite book
2787:894800884
2751:135890256
2685:Ross 1999
2670:Ross 1999
2532:18 August
2435:1747-1567
2285:τ
2255:π
2229:τ
2195:τ
2165:τ
2152:π
2137:γ
2129:τ
2085:τ
2075:π
2050:π
2037:
2025:τ
2015:π
1992:τ
1921:π
1908:
1896:τ
1889:τ
1796:Material
1722:σ
1682:−
1662:σ
1649:σ
1581:γ
1513:−
1486:τ
1483:Δ
1451:γ
1420:τ
1417:Δ
1382:ϵ
1291:τ
1257:ϵ
1230:τ
1227:Δ
1188:ρ
1158:σ
1132:ρ
1112:σ
1108:Δ
780:5000–9000
645:1150 (??)
564:Cast iron
448:A36 steel
431:Material
412:) with a
394:σ
381:σ
368:σ
346:pipelines
329:, unlike
308:aluminium
138:Corrosion
79:ϵ
55:σ
2854:19637912
2364:See also
2327:annealed
1557:particle
1524:particle
1433:particle
1210:alloying
839:550–620
831:Tungsten
825:240–370
817:Titanium
789:Tantalum
769:140–195
654:Silkworm
591:2014-T6
544:19.7–80
213:Yielding
163:Fracture
133:Buckling
2886:16 June
2824:Bibcode
2729:Bibcode
2564:15 June
2459:15 June
1303:is the
1028:Testing
940:MPa or
822:100–225
811:15–200
783:
775:Silicon
708:104–121
705:(limb)
662:
525:(HDPE)
338:ductile
273:plastic
269:elastic
158:Fouling
153:Fatigue
111:Offset
71:,
47:,
3059:
3044:
3026:
3009:
2990:
2975:
2956:
2934:
2913:
2852:
2834:
2785:
2775:
2749:
2626:
2433:
2213:τ
1949:where
1710:where
1283:where
1180:, and
1149:where
761:Nickel
752:80–100
733:40–50
690:UHMWPE
676:Twaron
672:Kevlar
668:Aramid
632:200+ ~
501:
441:(MPa)
436:(MPa)
281:stress
259:, the
173:Impact
69:strain
45:stress
2747:S2CID
2558:(PDF)
2551:(PDF)
2330:steel
1857:2.75
1835:0.49
1824:0.78
1813:0.37
766:14–35
730:15–20
684:3757
656:silk
648:1400
628:Brass
541:12–43
528:26–33
517:5650
491:1860
446:ASTM
416:or a
315:steel
298:is a
148:Creep
37:yield
3057:ISBN
3042:ISBN
3024:ISBN
3007:ISBN
2988:ISBN
2973:ISBN
2954:ISBN
2932:ISBN
2911:ISBN
2888:2024
2850:PMID
2801:link
2783:OCLC
2773:ISBN
2624:ISBN
2566:2011
2534:2010
2496:2010
2461:2011
2431:ISSN
1854:2.6
1846:3.2
1843:2.6
1832:1.4
1821:0.9
1810:1.0
1327:and
986:p0.2
953:p0.2
920:p0.1
808:9–14
797:200
755:350
744:210
711:130
703:Bone
681:3620
635:550
622:350
608:220
597:455
583:900
569:172
558:860
488:1650
480:760
473:A514
466:531
455:400
336:For
310:and
304:load
290:The
255:and
208:Wear
2842:doi
2737:doi
2653:doi
2423:doi
2289:max
2233:max
2215:max
2199:max
2169:max
2089:max
2034:cos
2029:max
1905:sin
1900:max
1873:max
1840:Ni
1829:Cu
1818:Al
1807:Ag
1208:By
961:350
928:310
836:550
803:Tin
794:180
722:75
697:35
674:or
659:500
619:130
594:400
580:830
555:520
531:37
477:690
463:448
452:250
355:In
333:.
294:or
251:In
3081::
2879:.
2862:^
2848:.
2840:.
2830:.
2818:.
2797:}}
2793:{{
2781:.
2759:^
2745:.
2735:.
2725:17
2723:.
2719:.
2677:^
2649:81
2647:.
2622:.
2620:61
2429:.
2419:47
2417:.
2413:.
2341:.
2317:.
2305:30
1875:.
1048:.
741:33
719:45
694:20
678:)
605:70
352:.
287:.
3065:.
3032:.
2998:.
2996:.
2964:.
2962:.
2942:.
2940:.
2919:.
2890:.
2856:.
2844::
2826::
2820:9
2803:)
2789:.
2753:.
2739::
2731::
2659:.
2655::
2632:.
2568:.
2536:.
2498:.
2463:.
2437:.
2425::
2301:/
2297:G
2294:=
2258:a
2252:2
2247:b
2244:G
2238:=
2159:b
2155:a
2149:2
2143:=
2134:d
2126:d
2120:=
2117:G
2079:b
2072:2
2066:=
2062:)
2057:b
2053:x
2047:2
2041:(
2019:b
2012:2
2006:=
2000:x
1997:d
1989:d
1983:=
1980:G
1957:b
1933:)
1928:b
1924:x
1918:2
1912:(
1892:=
1772:d
1750:k
1726:0
1690:2
1687:1
1678:d
1674:k
1671:+
1666:0
1658:=
1653:y
1609:l
1553:r
1520:r
1516:2
1504:l
1498:b
1495:G
1489:=
1439:l
1429:r
1423:=
1360:s
1356:C
1335:b
1315:G
1265:2
1262:3
1249:s
1245:C
1239:b
1236:G
1233:=
1162:y
1127:b
1124:G
1121:=
1116:y
982:R
958:=
949:R
925:=
916:R
900:)
670:(
398:3
390:,
385:2
377:,
372:1
240:e
233:t
226:v
43:(
23:.
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