Relation Between Strength and Hardness of High-Entropy Alloys

doi:10.1007/s40195-021-01252-y

Abstract

Abstract:

High-entropy alloys (HEAs) are composed of multiple principal elements and exhibit not only remarkable mechanical properties, but also promising potentials for developing numerous new compositions. To fully realize such potentials, high-throughput preparation and characterization technologies are especially useful; thereby, the fast evaluations of mechanical properties will be urgently required. Revealing the relation between strength and hardness is of significance for quickly predicting the strength of materials through simple hardness testing. However, up to now the strength-hardness relation for HEAs is still a puzzle. In this work, the relations between tensile or compressive strength and Vickers hardness of various HEAs with hundreds of compositions at room temperature are investigated, and finally, the solution for estimating the strengths of HEAs from their hardness values is achieved. Data for hundreds of different HEAs were extracted from studies reported in the period from 2010 to 2020. The results suggested that the well-known three-time relation (i.e., hardness equals to three times the magnitude of strength) works for nearly all HEAs, except for a few brittle HEAs which show quite high hardness but low strength due to early fracture. However, for HEAs with different phase structures, different strengths should be applied in using the 3-time relation, i.e., yield strength for low ductility body-centered cubic (BCC) HEAs and ultimate strength for highly plastic and work-hardenable face-centered cubic (FCC) HEAs. As for dual-phase or multi-phase HEAs, similar 3-time relations can be also found. The present approach sheds light on the mechanisms of hardness and also provides useful guidelines for quick estimation of strength from hardness for various HEAs.

Key words: High-entropy alloys, Vickers hardness, Strength, Plasticity

Xiaojuan Fan, Ruitao Qu, Zhefeng Zhang. Relation Between Strength and Hardness of High-Entropy Alloys[J]. Acta Metallurgica Sinica (English Letters), 2021, 34(11): 1461-1482.

Figures/Tables 17

References 98

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Alloy	Phase	H_V (MPa)	σ (MPa)		δ (%)	H_V/σ		R_t	Ref.
Alloy	Phase	H_V (MPa)	σ_y	σ_UTS	δ (%)	H_V/σ_y	H_V/σ_UTS	R_t	Ref.
Al₄(CoCrFeMnNi)₉₆	FCC	1657	217	500	58	7.64	3.31	2.30	[42]
Al₇(CoCrFeMnNi)₉₃	FCC	1785	242	529	47.2	7.38	3.37	2.19	[42]
Al_0.3CoCrFeNi	FCC	1403	180	419	63	7.79	3.35	2.33	[43]
AlCoCrFeNi₄	FCC	2185	312	660	39	7.00	3.31	2.12	[44]
Al₅Co₃₅Fe₂₀Ni₃₅Ti₅	FCC	3139	775	1045	18	4.05	3.0	1.35	[45]
C_2.2(Co₁₀Cr₁₀Fe₄₀Mn₄₀)_97.8	FCC	2087	310	650	62.9	6.73	3.21	2.10	[46]
C_3.3(Co₁₀Cr₁₀Fe₄₀Mn₄₀)_96.7	FCC	2411	422	787	77.8	5.71	3.06	1.86	[46]
C_4.4(Co₁₀Cr₁₀Fe₄₀Mn₄₀)_95.6	FCC	2646	467	836	54.7	5.67	3.16	1.79	[46]
Co₁₀Cr₁₀Fe₄₀Mn₄₀	FCC	1401	213	471	57.7	6.58	2.97	2.21	[46]
Co₅(CrFeMnNi)₉₅	FCC	1509	210	488	56.8	7.19	3.09	2.32	[47]
Co₁₀(CrFeMnNi)₉₀	FCC	1441	205	537	60.7	7.03	2.68	2.62	[47]
Co₂₀(CrFeMnNi)₈₀	FCC	1499	215	512	67.2	6.97	2.93	2.38	[47]
CoCrFeMnNi	FCC	1421	245	530	49.1	5.8	2.68	2.16	[44]
CoCrFeMnNi	FCC	1667	215	491	71	7.75	3.40	2.28	[7]
CoCrFeMnNi	FCC	1726	209	496	61.7	8.26	3.48	2.37	[42]
CoCrFeNi	FCC	1569	140	488	83	11.21	3.22	3.49	[7]
Co_0.5CrFeNi_1.5Ti_0.3	FCC	3038	586	875	46	5.18	3.47	1.49	[48]
CoCrFeNiTi_0.3	FCC	2577	540	772	60	4.77	3.34	1.43	[48]
CoCu_0.5FeNiTa_0.1	FCC	1836	315	575	36.3	5.83	3.19	1.83	[49]
CrFeNi₂Ti_0.3	FCC	3283	672	982	37	4.89	3.34	1.46	[48]
Al₁₈Co₂₀Cr₂₁Fe₂₀Ni₂₁	BCC	4978	-	355	0	-	14.02	-	[50]
Hf_0.5Nb_0.5Ta_0.5Ti_1.5Zr	BCC	2950	903	990	18.8	3.27	2.98	1.10	[16]
HfNbTaTiZr	BCC	3518	1155	1212	12.3	3.05	2.90	1.05	[51]
NbTaTi	BCC	2411	620	683	18.5	3.89	3.53	1.10	[51]
NbTiZr	BCC	2891	956	991	14.2	3.02	2.92	1.04	[51]
Al₈(CoCrFeMnNi)₉₂	FCC + BCC	1775	281	644	36.5	6.32	2.76	2.29	[42]
Al₉(CoCrFeMnNi)₉₁	FCC + BCC	2141	331	727	30.4	6.47	2.94	2.20	[42]
Al₁₀(CoCrFeMnNi)₉₀	FCC + BCC	2707	526	994	18.8	5.15	2.72	1.89	[42]
Al₁₁(CoCrFeMnNi)₈₉	FCC + BCC	3949	832	1174	7.7	4.75	3.36	1.41	[42]
Al_0.5CoCrFeNi	FCC + BCC	2744	380	810	67	7.22	3.39	2.13	[52]
AlCoCrFeNi_1.5	FCC + BCC	4904	795	1150	3.1	6.17	4.26	1.45	[44]
AlCoCrFeNi₂	FCC + BCC	3236	680	1130	21.2	4.76	2.86	1.66	[44]
AlCoCrFeNi_2.5	FCC + BCC	2567	470	900	25.3	5.46	2.85	1.91	[44]
AlCoCrFeNi₃	FCC + BCC	2344	387	810	31.2	6.06	2.89	2.09	[44]
Al_10.5Co₂₀Cr_24.75Fe₂₀Ni_24.75	FCC + BCC	2401	370	790	25	6.49	3.04	2.14	[50]
CoCrFeMn	FCC + IM	5194	338	795	4.3	15.4	6.53	2.35	[44]
(CoCrFeMn)₉₀Ni₁₀	FCC + IM	1509	246	450	18.2	6.13	3.35	1.83	[44]
CoCrFeMnNiV	FCC + IM	6375	-	90	0	-	70.83	-	[7]
CoCrFeNiV	FCC + IM	5139	-	311	0	-	16.52	-	[7]
CoCuFeMnNiSn_0.05	FCC + IM	1999.2	283	477	10.1	7.06	4.19	1.69	[53]
CoCuFeMnNiSn_0.08	FCC + IM	2126.6	272	424	6.3	7.82	5.02	1.56	[53]
CoCuFeMnNiSn_0.1	FCC + IM	2459.8	333	472	5.1	7.39	5.21	1.42	[53]
CoCuFeMnNiSn_0.2	FCC + IM	3116.4	283	368	1.7	11.0	8.47	1.30	[53]

Alloy	Phase	H_V (MPa)	σ (MPa)		δ (%)	H_V/σ		R_t	Ref.
Alloy	Phase	H_V (MPa)	σ_y	σ_UTS	δ (%)	H_V/σ_y	H_V/σ_UTS	R_t	Ref.
Al₄(CoCrFeMnNi)₉₆	FCC	1657	217	500	58	7.64	3.31	2.30	[42]
Al₇(CoCrFeMnNi)₉₃	FCC	1785	242	529	47.2	7.38	3.37	2.19	[42]
Al_0.3CoCrFeNi	FCC	1403	180	419	63	7.79	3.35	2.33	[43]
AlCoCrFeNi₄	FCC	2185	312	660	39	7.00	3.31	2.12	[44]
Al₅Co₃₅Fe₂₀Ni₃₅Ti₅	FCC	3139	775	1045	18	4.05	3.0	1.35	[45]
C_2.2(Co₁₀Cr₁₀Fe₄₀Mn₄₀)_97.8	FCC	2087	310	650	62.9	6.73	3.21	2.10	[46]
C_3.3(Co₁₀Cr₁₀Fe₄₀Mn₄₀)_96.7	FCC	2411	422	787	77.8	5.71	3.06	1.86	[46]
C_4.4(Co₁₀Cr₁₀Fe₄₀Mn₄₀)_95.6	FCC	2646	467	836	54.7	5.67	3.16	1.79	[46]
Co₁₀Cr₁₀Fe₄₀Mn₄₀	FCC	1401	213	471	57.7	6.58	2.97	2.21	[46]
Co₅(CrFeMnNi)₉₅	FCC	1509	210	488	56.8	7.19	3.09	2.32	[47]
Co₁₀(CrFeMnNi)₉₀	FCC	1441	205	537	60.7	7.03	2.68	2.62	[47]
Co₂₀(CrFeMnNi)₈₀	FCC	1499	215	512	67.2	6.97	2.93	2.38	[47]
CoCrFeMnNi	FCC	1421	245	530	49.1	5.8	2.68	2.16	[44]
CoCrFeMnNi	FCC	1667	215	491	71	7.75	3.40	2.28	[7]
CoCrFeMnNi	FCC	1726	209	496	61.7	8.26	3.48	2.37	[42]
CoCrFeNi	FCC	1569	140	488	83	11.21	3.22	3.49	[7]
Co_0.5CrFeNi_1.5Ti_0.3	FCC	3038	586	875	46	5.18	3.47	1.49	[48]
CoCrFeNiTi_0.3	FCC	2577	540	772	60	4.77	3.34	1.43	[48]
CoCu_0.5FeNiTa_0.1	FCC	1836	315	575	36.3	5.83	3.19	1.83	[49]
CrFeNi₂Ti_0.3	FCC	3283	672	982	37	4.89	3.34	1.46	[48]
Al₁₈Co₂₀Cr₂₁Fe₂₀Ni₂₁	BCC	4978	-	355	0	-	14.02	-	[50]
Hf_0.5Nb_0.5Ta_0.5Ti_1.5Zr	BCC	2950	903	990	18.8	3.27	2.98	1.10	[16]
HfNbTaTiZr	BCC	3518	1155	1212	12.3	3.05	2.90	1.05	[51]
NbTaTi	BCC	2411	620	683	18.5	3.89	3.53	1.10	[51]
NbTiZr	BCC	2891	956	991	14.2	3.02	2.92	1.04	[51]
Al₈(CoCrFeMnNi)₉₂	FCC + BCC	1775	281	644	36.5	6.32	2.76	2.29	[42]
Al₉(CoCrFeMnNi)₉₁	FCC + BCC	2141	331	727	30.4	6.47	2.94	2.20	[42]
Al₁₀(CoCrFeMnNi)₉₀	FCC + BCC	2707	526	994	18.8	5.15	2.72	1.89	[42]
Al₁₁(CoCrFeMnNi)₈₉	FCC + BCC	3949	832	1174	7.7	4.75	3.36	1.41	[42]
Al_0.5CoCrFeNi	FCC + BCC	2744	380	810	67	7.22	3.39	2.13	[52]
AlCoCrFeNi_1.5	FCC + BCC	4904	795	1150	3.1	6.17	4.26	1.45	[44]
AlCoCrFeNi₂	FCC + BCC	3236	680	1130	21.2	4.76	2.86	1.66	[44]
AlCoCrFeNi_2.5	FCC + BCC	2567	470	900	25.3	5.46	2.85	1.91	[44]
AlCoCrFeNi₃	FCC + BCC	2344	387	810	31.2	6.06	2.89	2.09	[44]
Al_10.5Co₂₀Cr_24.75Fe₂₀Ni_24.75	FCC + BCC	2401	370	790	25	6.49	3.04	2.14	[50]
CoCrFeMn	FCC + IM	5194	338	795	4.3	15.4	6.53	2.35	[44]
(CoCrFeMn)₉₀Ni₁₀	FCC + IM	1509	246	450	18.2	6.13	3.35	1.83	[44]
CoCrFeMnNiV	FCC + IM	6375	-	90	0	-	70.83	-	[7]
CoCrFeNiV	FCC + IM	5139	-	311	0	-	16.52	-	[7]
CoCuFeMnNiSn_0.05	FCC + IM	1999.2	283	477	10.1	7.06	4.19	1.69	[53]
CoCuFeMnNiSn_0.08	FCC + IM	2126.6	272	424	6.3	7.82	5.02	1.56	[53]
CoCuFeMnNiSn_0.1	FCC + IM	2459.8	333	472	5.1	7.39	5.21	1.42	[53]
CoCuFeMnNiSn_0.2	FCC + IM	3116.4	283	368	1.7	11.0	8.47	1.30	[53]

Alloy	Phase	H_V (MPa)	σ (MPa)			ε_f (%)	H_V/σ			R_c or R_c10	Ref.
Alloy	Phase	H_V (MPa)	σ_yc	σ₁₀	σ_f	ε_f (%)	H_V/σ_yc	H_V/σ₁₀	H_V/σ_f	R_c or R_c10	Ref.
Al_0.4CoCrFeNi	FCC	1525	233	420	-	81.3	6.55	3.63	-	1.80	[54]
Al_0.5CoCrFeNi	FCC	1697	138	638	-	> 28	12.29	2.66	-	4.62	[8]
Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄	FCC	1471	249	473	-	> 50	5.91	3.11	-	1.90	[55]
Al_0.5CoCrFeMo_0.1Ni	FCC	2207	184	770	-	> 28	11.99	2.87	-	4.18	[8]
Al_0.2CoCrFeNiTi_0.5	FCC	4698	1320	1691	1681	19.5	3.56	2.78	2.79	1.27	[56]
CoCrFeMnNi	FCC	1323	230	441	-	> 75	5.75	3.00	-	1.92	[57]
CoCrFeNi	FCC	1315	190	400	-	> 75	6.92	3.29	-	2.11	[7]
CoCrFeNiTi_0.5	FCC	4972	1147	1595	1589	22	4.33	3.12	3.13	1.39	[56]
CoFeNi	FCC	1195	199	419	-	> 50	6.01	2.85	-	2.11	[58]
CoFeNiSi_0.25	FCC	1434	189	396	-	> 50	7.59	3.62	-	2.10	[58]
CoFeNiV	FCC	2335	428	747	-	> 80	5.46	3.13	-	1.75	[59]
AlCoCrFeNi	BCC	4782	1350	1597	2210	24.2	3.54	2.99	2.16	1.64	[60]
AlCoCrFeNi	BCC	5096	1373	1930	2609	28.1	3.71	2.64	1.95	1.90	[61]
AlCoCrFeNi	BCC	5237	1379	1742	2149	27	3.8	3.00	2.44	1.56	[62]
AlCoCrFeNiV_0.2	BCC	5468	1492	1742	2309	32	3.67	3.14	2.37	1.55	[62]
AlCoCrFeNiV_0.5	BCC	5799	1598	-	1754	10	3.63	-	3.31	1.1	[62]
AlCoCrFeNiV_0.8	BCC	6127	1696	-	1866	13	3.61	-	3.28	1.10	[62]
AlCoCrFeNiV	BCC	6363	1727	-	1764	7.5	3.68	-	3.61	1.02	[62]
AlCoCrFeNiV	BCC	6520	-	-	1801	6.4	-	-	3.62	-	[63]
Al_1.5CoCrFeNiV	BCC	6712	-	-	1980	9.5	-	-	3.39	-	[63]
AlCoFeNi	BCC	4410	967	-	1257	7.9	4.56	-	3.51	1.30	[58]
Al_0.3HfNbTaTiZr	BCC	3459	1188	1324	-	> 50	2.91	2.61	-	1.11	[64]
Al_0.4Hf_0.6NbTaTiZr	BCC	4900	1841	-	2087	10	2.66	-	2.35	1.13	[65]
Al_0.4Hf_0.6NbTaTiZr	BCC	4000	1280	-	1319	3.5	3.1	-	3.03	1.03	[66]
Al_0.5HfNbTaTiZr	BCC	3881	1302	1510	-	46	2.98	2.57	-	1.16	[64]
Al_0.75HfNbTaTiZr	BCC	4185	1415	1555	1520	30	2.96	2.69	2.75	1.07	[64]
AlHfNbTaTiZr	BCC	4322	1489	1649	1544	21	2.90	2.62	2.80	1.04	[64]
Al_0.25MoNbTiV	BCC	4509	1250	-	1362	12.9	3.61	-	3.31	1.09	[67]
Al_0.5MoNbTiV	BCC	4768	1625	-	1670	11.3	2.93	-	2.86	1.03	[67]
Al_0.3NbTa_0.8Ti_1.4V_0.2Zr_1.3	BCC	4900	1965	-	1957	5	2.49	-	2.50	0.99	[66]
AlNb_1.5Ta_0.5Ti_1.5Zr_0.5	BCC	4900	1841	-	2042	10	2.66	-	2.40	1.11	[66]
AlNbTiV	BCC	4315	1020	-	1278	5	4.23	-	3.38	1.25	[68]
HfMo_0.25NbTaTiZr	BCC	3871	1112	1328	-	> 50	3.48	2.91	-	1.19	[69]
HfMo_0.5NbTaTiZr	BCC	4704	1317	1535	-	> 50	3.57	3.07	-	1.17	[69]
HfMo_0.75NbTaTiZr	BCC	4822	1373	1585	-	> 50	3.51	3.04	-	1.15	[69]
HfMoNbTaTiZr	BCC	4949	1512	-	1625	12	3.27	-	3.05	1.07	[69]
HfMoNbTaTiZr	BCC	4952	1512	-	1653	12	3.27	-	3.00	1.09	[70]
HfMoTaTiZr	BCC	5315	1600	-	1709	4	3.32	-	3.10	1.06	[70]
HfNbTaTiZr	BCC	3283	1015	1165	-	> 50	3.23	2.82	-	1.15	[69]
HfNbTaTiZr	BCC	3826	929	1248	-	> 50	4.12	3.07	-	1.34	[71]
HfNbTaTiZr	BCC	2891	1073	1221	-	> 50	2.69	2.37	-	1.14	[64]
HfNbTaZr	BCC	3575	1315	1501	1447	25	2.72	2.38	2.47	1.10	[72]
MoNbTaV	BCC	4947	1525	1869	1968	21	3.24	2.65	2.51	1.29	[73]
MoNbTiV	BCC	4319	1200	1501	1593	25.6	3.6	2.88	2.71	1.33	[67]
NbTaTiV	BCC	3113	965	1107	-	> 50	3.23	3.07	-	1.05	[74]
NbTaTiVW	BCC	4380	1420	1748	1776	22	3.08	2.73	2.99	1.03	[74]
NbTaVW	BCC	4830	1530	-	1621	13	3.16	-	3.19	0.99	[74]
AlCoCrCuFeNi	FCC + BCC	5056	1515	1627	1638	20.7	3.34	3.11	3.09	1.08	[75]
AlCoCrCuFeNi	FCC + BCC	4629	1227	1404	1510	16	3.77	3.3	3.07	1.23	[76]
AlCoCrFeMnNi	FCC + BCC	6492	-	-	2142	8.3	-	-	3.03	-	[77]
Al_0.4Co_0.25CrFeNi	FCC + BCC	2013	522	603	-	75.1	3.86	3.34	-	1.16	[54]
Al_0.7Co_0.3CrFeNi	FCC + BCC	6119	2033	-	2453	8.1	3.01	-	2.49	1.21	[78]
AlCoCrFeNi_1.5	FCC + BCC	5135	1360	1930	2114	20.8	3.78	2.66	2.43	1.55	[60]
AlCoCrFeNi_1.8	FCC + BCC	3312	600	1129	1591	37.6	5.52	2.93	2.08	2.65	[60]
AlCoCrFeNi_2.1	FCC + BCC	2920	670	1047	-	> 60	4.36	2.79	-	1.56	[60]
AlCoCrFeNi_2.4	FCC + BCC	2646	500	877	1446	42.5	5.29	3.02	1.83	2.89	[60]
AlCoCrFeNi_2.7	FCC + BCC	2548	470	780	1470	49.3	5.42	3.27	1.73	3.13	[60]
AlCoCrFeNi₃	FCC + BCC	2362	440	744	1364	44.7	5.37	3.17	1.73	3.1	[60]
(Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄)₈₉Cr₁₁	FCC + BCC	2942	456	812	-	> 50	6.45	3.62	-	1.78	[55]
(Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄)₈₀Cr₂₀	FCC + BCC	4119	998	1302	1191	29.5	4.13	3.16	3.46	1.19	[55]
(Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄)₇₄Cr₂₆	FCC + BCC	5002	1649	2024	2233	24.9	3.03	2.47	2.24	1.35	[55]
Al_0.5CoCrFeNiTi_0.5	FCC + BCC	5227	1709	-	1977	13.5	3.06	-	2.64	1.16	[56]
Al_0.5CoCrFeNiTi_0.5	FCC + BCC	5104	1100	1612	1699	27.5	4.64	3.17	3.00	1.54	[79]
Al_0.8CoCrFeNiTi_0.2	FCC + BCC	4635	968	1598	1780	30.1	4.79	2.90	2.60	1.84	[79]
Al_0.5CoCrFeNiV	FCC + BCC	6217	-	-	1761	8.2	-	-	3.53	-	[63]
AlCoCuFeMnNi	FCC + BCC	4394	1317	-	1723	12.8	3.33	-	2.57	1.31	[80]
AlCoCuFeNi	FCC + BCC	5259	1134	-	1330	9	4.64	-	3.95	1.17	[76]
AlCoCuFeNi	FCC + BCC	5211	1210	-	1330	8.7	4.31	-	3.91	1.1	[81]
AlCoCuFeNiSi	FCC + BCC	6673	1712	-	1930	10	3.90	-	3.46	1.13	[76]
AlCoCuFeNiTi	FCC + BCC	6132	1366	-	1660	11	4.49	-	3.69	1.22	[76]
Al_0.5CoFeNi	FCC + BCC	1999	343	563	-	> 50	5.83	3.55	-	1.64	[58]
Al_0.6CoFeNi	FCC + BCC	6541	2200	-	2322	6.2	2.97	-	2.82	1.06	[82]
Al_0.75CoFeNi	FCC + BCC	3731	786	1435	1955	31.2	4.75	2.6	1.90	2.49	[58]
Al_0.6CoFeNiTi_0.4	FCC + BCC	6982	2732	-	2915	10.1	2.56		2.4	1.07	[83]
CoCrFeMnNiV_{0. 5}	FCC + IM	2695	620	904	-	> 75	4.35	2.98	-	1.46	[57]
CoCrFeMnNiV_0.75	FCC + IM	3724	740	-	1248	7.8	5.03	-	2.99	1.69	[57]
CoCrFeMnNiV	FCC + IM	6233	1660	-	1845	0.5	3.75	-	3.38	1.12	[57]
CoCrFeMnNiV	FCC + IM	6239	1660	-	1845	0.5	3.76	-	3.38	1.11	[7]
CoCrFeMo_0.5Ni	FCC + IM	3128	510	1017	1371	33	6.13	3.07	2.28	2.69	[84]
CoCrFeMo_0.85Ni	FCC + IM	4119	929	-	1441	21	4.43	-	2.86	1.55	[84]
Co_0.5CrFeNiTi_0.5	FCC + IM	8460	2650	-	2690	10	3.19	-	3.14	1.02	[85]
CoCrFeNiV	FCC + IM	5758	1435	-	1656	2.5	4.01	-	3.48	1.15	[7]
CoCrFeNiV	FCC + IM	4770	1176	-	1572	9.7	4.06	-	3.03	1.34	[63]
CoFeMo_0.2NiV	FCC + IM	2621	687	748	-	> 80	3.82	3.50	-	1.09	[59]
CoFeMo_0.4NiV	FCC + IM	3947	1000	1432	1649	25	3.95	2.76	2.39	1.65	[59]
CoFeMo_0.6NiV	FCC + IM	5459	1589	-	2038	< 5	3.44	-	2.68	1.28	[59]
CoFeMo_0.8NiV	FCC + IM	5939	1770	-	2164	< 5	3.36	-	2.75	1.22	[59]
CoFeMoNiV	FCC + IM	6121	1963	-	1963	< 5	3.12	-	3.12	1	[59]
CoFeMoNi_1.2 V	FCC + IM	5900	1971	-	1847	8.3	2.99	-	3.19	0.94	[59]
CoFeMoNi_1.4 V	FCC + IM	5268	1505	-	1756	8.9	3.50	-	3	1.17	[59]
CoFeMoNi_1.6 V	FCC + IM	5010	1443	-	1770	8.7	3.47	-	2.83	1.23	[59]
CoFeMoNi_1.8 V	FCC + IM	5001	1330	-	1797	10.3	3.76	-	2.78	1.35	[59]
CoFeNiSi_0.5	FCC + IM	2759	472	925	1388	44	5.85	2.98	1.99	2.94	[58]
CoFeNiSi_0.75	FCC + IM	5566	1297	-	1906	2.9	4.29	-	2.92	1.47	[58]
Al₂CoCrFeNiV	BCC + IM	6393	-	-	1802	4.3	-	-	3.55	-	[63]
AlCrFeMo_0.8Ni	BCC + IM	8376	-	-	1512	0	-	-	5.54	-	[9]
CrFeMoNbV	BCC + IM	8100	2663	-	2615	2.7	3.04	-	3.10	0.98	[86]
CrMo_0.5NbTiV	BCC + IM	5080	1610	-	1628	6.4	3.16	-	3.12	1.01	[87]
Cr_1.5Mo_0.5NbTiV	BCC + IM	5678	1897	-	1892	4.5	2.99	-	3.00	0.99	[87]
Cr₂Mo_0.5NbTiV	BCC + IM	6541	2311	-	2285	3.3	2.83	-	2.86	0.99	[87]
CrNbTiVZr	BCC + IM	4720	-	-	1298	3	-	-	3.64	-	[88]
CrNbTiZr	BCC + IM	4099	-	-	1260	6	-	-	3.25	-	[88]
HfNbSi_0.5TiV	BCC + IM	4802	1399	-	1465	10.9	3.43	-	3.28	1.05	[89]
Al_0.5CoCrFeMo_0.2Ni	FCC + BCC + IM	2785	556	1110	1357	34	5.01	2.51	2.05	2.44	[8]
Al_0.5CoCrFeMo_0.3Ni	FCC + BCC + IM	3325	814	1282	1529	31	4.08	2.59	2.17	1.88	[8]
Al_0.5CoCrFeMo_0.4Ni	FCC + BCC + IM	4286	1091	1664	1810	18	3.93	2.58	2.37	1.66	[8]
Al_0.5CoCrFeMo_0.5Ni	FCC + BCC + IM	5570	1544	-	2242	10	3.61	-	2.48	1.45	[8]
Al_0.5CoFeNiTi_0.5	FCC + BCC + IM	7188	-	-	2850	1.6	-	-	2.52	-	[90]
AlCrCuFeNi_0.6	FCC + BCC + IM	4848	1496	-	2025	2.87	3.24	-	2.39	1.35	[91]
AlCrCuFeNi	FCC + BCC + IM	4844	1496	-	1800	1.9	3.24	-	2.69	1.20	[91]
AlCrCuFeNi_1.2	FCC + BCC + IM	3998	1105	-	1298	1.4	3.62	-	3.08	1.17	[91]
AlCrCuFeNi_1.4	FCC + BCC + IM	3626	1265	-	1707	2.2	2.87	-	2.12	1.35	[91]

Alloy	Phase	H_V (MPa)	σ (MPa)			ε_f (%)	H_V/σ			R_c or R_c10	Ref.
Alloy	Phase	H_V (MPa)	σ_yc	σ₁₀	σ_f	ε_f (%)	H_V/σ_yc	H_V/σ₁₀	H_V/σ_f	R_c or R_c10	Ref.
Al_0.4CoCrFeNi	FCC	1525	233	420	-	81.3	6.55	3.63	-	1.80	[54]
Al_0.5CoCrFeNi	FCC	1697	138	638	-	> 28	12.29	2.66	-	4.62	[8]
Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄	FCC	1471	249	473	-	> 50	5.91	3.11	-	1.90	[55]
Al_0.5CoCrFeMo_0.1Ni	FCC	2207	184	770	-	> 28	11.99	2.87	-	4.18	[8]
Al_0.2CoCrFeNiTi_0.5	FCC	4698	1320	1691	1681	19.5	3.56	2.78	2.79	1.27	[56]
CoCrFeMnNi	FCC	1323	230	441	-	> 75	5.75	3.00	-	1.92	[57]
CoCrFeNi	FCC	1315	190	400	-	> 75	6.92	3.29	-	2.11	[7]
CoCrFeNiTi_0.5	FCC	4972	1147	1595	1589	22	4.33	3.12	3.13	1.39	[56]
CoFeNi	FCC	1195	199	419	-	> 50	6.01	2.85	-	2.11	[58]
CoFeNiSi_0.25	FCC	1434	189	396	-	> 50	7.59	3.62	-	2.10	[58]
CoFeNiV	FCC	2335	428	747	-	> 80	5.46	3.13	-	1.75	[59]
AlCoCrFeNi	BCC	4782	1350	1597	2210	24.2	3.54	2.99	2.16	1.64	[60]
AlCoCrFeNi	BCC	5096	1373	1930	2609	28.1	3.71	2.64	1.95	1.90	[61]
AlCoCrFeNi	BCC	5237	1379	1742	2149	27	3.8	3.00	2.44	1.56	[62]
AlCoCrFeNiV_0.2	BCC	5468	1492	1742	2309	32	3.67	3.14	2.37	1.55	[62]
AlCoCrFeNiV_0.5	BCC	5799	1598	-	1754	10	3.63	-	3.31	1.1	[62]
AlCoCrFeNiV_0.8	BCC	6127	1696	-	1866	13	3.61	-	3.28	1.10	[62]
AlCoCrFeNiV	BCC	6363	1727	-	1764	7.5	3.68	-	3.61	1.02	[62]
AlCoCrFeNiV	BCC	6520	-	-	1801	6.4	-	-	3.62	-	[63]
Al_1.5CoCrFeNiV	BCC	6712	-	-	1980	9.5	-	-	3.39	-	[63]
AlCoFeNi	BCC	4410	967	-	1257	7.9	4.56	-	3.51	1.30	[58]
Al_0.3HfNbTaTiZr	BCC	3459	1188	1324	-	> 50	2.91	2.61	-	1.11	[64]
Al_0.4Hf_0.6NbTaTiZr	BCC	4900	1841	-	2087	10	2.66	-	2.35	1.13	[65]
Al_0.4Hf_0.6NbTaTiZr	BCC	4000	1280	-	1319	3.5	3.1	-	3.03	1.03	[66]
Al_0.5HfNbTaTiZr	BCC	3881	1302	1510	-	46	2.98	2.57	-	1.16	[64]
Al_0.75HfNbTaTiZr	BCC	4185	1415	1555	1520	30	2.96	2.69	2.75	1.07	[64]
AlHfNbTaTiZr	BCC	4322	1489	1649	1544	21	2.90	2.62	2.80	1.04	[64]
Al_0.25MoNbTiV	BCC	4509	1250	-	1362	12.9	3.61	-	3.31	1.09	[67]
Al_0.5MoNbTiV	BCC	4768	1625	-	1670	11.3	2.93	-	2.86	1.03	[67]
Al_0.3NbTa_0.8Ti_1.4V_0.2Zr_1.3	BCC	4900	1965	-	1957	5	2.49	-	2.50	0.99	[66]
AlNb_1.5Ta_0.5Ti_1.5Zr_0.5	BCC	4900	1841	-	2042	10	2.66	-	2.40	1.11	[66]
AlNbTiV	BCC	4315	1020	-	1278	5	4.23	-	3.38	1.25	[68]
HfMo_0.25NbTaTiZr	BCC	3871	1112	1328	-	> 50	3.48	2.91	-	1.19	[69]
HfMo_0.5NbTaTiZr	BCC	4704	1317	1535	-	> 50	3.57	3.07	-	1.17	[69]
HfMo_0.75NbTaTiZr	BCC	4822	1373	1585	-	> 50	3.51	3.04	-	1.15	[69]
HfMoNbTaTiZr	BCC	4949	1512	-	1625	12	3.27	-	3.05	1.07	[69]
HfMoNbTaTiZr	BCC	4952	1512	-	1653	12	3.27	-	3.00	1.09	[70]
HfMoTaTiZr	BCC	5315	1600	-	1709	4	3.32	-	3.10	1.06	[70]
HfNbTaTiZr	BCC	3283	1015	1165	-	> 50	3.23	2.82	-	1.15	[69]
HfNbTaTiZr	BCC	3826	929	1248	-	> 50	4.12	3.07	-	1.34	[71]
HfNbTaTiZr	BCC	2891	1073	1221	-	> 50	2.69	2.37	-	1.14	[64]
HfNbTaZr	BCC	3575	1315	1501	1447	25	2.72	2.38	2.47	1.10	[72]
MoNbTaV	BCC	4947	1525	1869	1968	21	3.24	2.65	2.51	1.29	[73]
MoNbTiV	BCC	4319	1200	1501	1593	25.6	3.6	2.88	2.71	1.33	[67]
NbTaTiV	BCC	3113	965	1107	-	> 50	3.23	3.07	-	1.05	[74]
NbTaTiVW	BCC	4380	1420	1748	1776	22	3.08	2.73	2.99	1.03	[74]
NbTaVW	BCC	4830	1530	-	1621	13	3.16	-	3.19	0.99	[74]
AlCoCrCuFeNi	FCC + BCC	5056	1515	1627	1638	20.7	3.34	3.11	3.09	1.08	[75]
AlCoCrCuFeNi	FCC + BCC	4629	1227	1404	1510	16	3.77	3.3	3.07	1.23	[76]
AlCoCrFeMnNi	FCC + BCC	6492	-	-	2142	8.3	-	-	3.03	-	[77]
Al_0.4Co_0.25CrFeNi	FCC + BCC	2013	522	603	-	75.1	3.86	3.34	-	1.16	[54]
Al_0.7Co_0.3CrFeNi	FCC + BCC	6119	2033	-	2453	8.1	3.01	-	2.49	1.21	[78]
AlCoCrFeNi_1.5	FCC + BCC	5135	1360	1930	2114	20.8	3.78	2.66	2.43	1.55	[60]
AlCoCrFeNi_1.8	FCC + BCC	3312	600	1129	1591	37.6	5.52	2.93	2.08	2.65	[60]
AlCoCrFeNi_2.1	FCC + BCC	2920	670	1047	-	> 60	4.36	2.79	-	1.56	[60]
AlCoCrFeNi_2.4	FCC + BCC	2646	500	877	1446	42.5	5.29	3.02	1.83	2.89	[60]
AlCoCrFeNi_2.7	FCC + BCC	2548	470	780	1470	49.3	5.42	3.27	1.73	3.13	[60]
AlCoCrFeNi₃	FCC + BCC	2362	440	744	1364	44.7	5.37	3.17	1.73	3.1	[60]
(Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄)₈₉Cr₁₁	FCC + BCC	2942	456	812	-	> 50	6.45	3.62	-	1.78	[55]
(Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄)₈₀Cr₂₀	FCC + BCC	4119	998	1302	1191	29.5	4.13	3.16	3.46	1.19	[55]
(Al₇Co₂₄Cr₂₁Fe₂₄Ni₂₄)₇₄Cr₂₆	FCC + BCC	5002	1649	2024	2233	24.9	3.03	2.47	2.24	1.35	[55]
Al_0.5CoCrFeNiTi_0.5	FCC + BCC	5227	1709	-	1977	13.5	3.06	-	2.64	1.16	[56]
Al_0.5CoCrFeNiTi_0.5	FCC + BCC	5104	1100	1612	1699	27.5	4.64	3.17	3.00	1.54	[79]
Al_0.8CoCrFeNiTi_0.2	FCC + BCC	4635	968	1598	1780	30.1	4.79	2.90	2.60	1.84	[79]
Al_0.5CoCrFeNiV	FCC + BCC	6217	-	-	1761	8.2	-	-	3.53	-	[63]
AlCoCuFeMnNi	FCC + BCC	4394	1317	-	1723	12.8	3.33	-	2.57	1.31	[80]
AlCoCuFeNi	FCC + BCC	5259	1134	-	1330	9	4.64	-	3.95	1.17	[76]
AlCoCuFeNi	FCC + BCC	5211	1210	-	1330	8.7	4.31	-	3.91	1.1	[81]
AlCoCuFeNiSi	FCC + BCC	6673	1712	-	1930	10	3.90	-	3.46	1.13	[76]
AlCoCuFeNiTi	FCC + BCC	6132	1366	-	1660	11	4.49	-	3.69	1.22	[76]
Al_0.5CoFeNi	FCC + BCC	1999	343	563	-	> 50	5.83	3.55	-	1.64	[58]
Al_0.6CoFeNi	FCC + BCC	6541	2200	-	2322	6.2	2.97	-	2.82	1.06	[82]
Al_0.75CoFeNi	FCC + BCC	3731	786	1435	1955	31.2	4.75	2.6	1.90	2.49	[58]
Al_0.6CoFeNiTi_0.4	FCC + BCC	6982	2732	-	2915	10.1	2.56		2.4	1.07	[83]
CoCrFeMnNiV_{0. 5}	FCC + IM	2695	620	904	-	> 75	4.35	2.98	-	1.46	[57]
CoCrFeMnNiV_0.75	FCC + IM	3724	740	-	1248	7.8	5.03	-	2.99	1.69	[57]
CoCrFeMnNiV	FCC + IM	6233	1660	-	1845	0.5	3.75	-	3.38	1.12	[57]
CoCrFeMnNiV	FCC + IM	6239	1660	-	1845	0.5	3.76	-	3.38	1.11	[7]
CoCrFeMo_0.5Ni	FCC + IM	3128	510	1017	1371	33	6.13	3.07	2.28	2.69	[84]
CoCrFeMo_0.85Ni	FCC + IM	4119	929	-	1441	21	4.43	-	2.86	1.55	[84]
Co_0.5CrFeNiTi_0.5	FCC + IM	8460	2650	-	2690	10	3.19	-	3.14	1.02	[85]
CoCrFeNiV	FCC + IM	5758	1435	-	1656	2.5	4.01	-	3.48	1.15	[7]
CoCrFeNiV	FCC + IM	4770	1176	-	1572	9.7	4.06	-	3.03	1.34	[63]
CoFeMo_0.2NiV	FCC + IM	2621	687	748	-	> 80	3.82	3.50	-	1.09	[59]
CoFeMo_0.4NiV	FCC + IM	3947	1000	1432	1649	25	3.95	2.76	2.39	1.65	[59]
CoFeMo_0.6NiV	FCC + IM	5459	1589	-	2038	< 5	3.44	-	2.68	1.28	[59]
CoFeMo_0.8NiV	FCC + IM	5939	1770	-	2164	< 5	3.36	-	2.75	1.22	[59]
CoFeMoNiV	FCC + IM	6121	1963	-	1963	< 5	3.12	-	3.12	1	[59]
CoFeMoNi_1.2 V	FCC + IM	5900	1971	-	1847	8.3	2.99	-	3.19	0.94	[59]
CoFeMoNi_1.4 V	FCC + IM	5268	1505	-	1756	8.9	3.50	-	3	1.17	[59]
CoFeMoNi_1.6 V	FCC + IM	5010	1443	-	1770	8.7	3.47	-	2.83	1.23	[59]
CoFeMoNi_1.8 V	FCC + IM	5001	1330	-	1797	10.3	3.76	-	2.78	1.35	[59]
CoFeNiSi_0.5	FCC + IM	2759	472	925	1388	44	5.85	2.98	1.99	2.94	[58]
CoFeNiSi_0.75	FCC + IM	5566	1297	-	1906	2.9	4.29	-	2.92	1.47	[58]
Al₂CoCrFeNiV	BCC + IM	6393	-	-	1802	4.3	-	-	3.55	-	[63]
AlCrFeMo_0.8Ni	BCC + IM	8376	-	-	1512	0	-	-	5.54	-	[9]
CrFeMoNbV	BCC + IM	8100	2663	-	2615	2.7	3.04	-	3.10	0.98	[86]
CrMo_0.5NbTiV	BCC + IM	5080	1610	-	1628	6.4	3.16	-	3.12	1.01	[87]
Cr_1.5Mo_0.5NbTiV	BCC + IM	5678	1897	-	1892	4.5	2.99	-	3.00	0.99	[87]
Cr₂Mo_0.5NbTiV	BCC + IM	6541	2311	-	2285	3.3	2.83	-	2.86	0.99	[87]
CrNbTiVZr	BCC + IM	4720	-	-	1298	3	-	-	3.64	-	[88]
CrNbTiZr	BCC + IM	4099	-	-	1260	6	-	-	3.25	-	[88]
HfNbSi_0.5TiV	BCC + IM	4802	1399	-	1465	10.9	3.43	-	3.28	1.05	[89]
Al_0.5CoCrFeMo_0.2Ni	FCC + BCC + IM	2785	556	1110	1357	34	5.01	2.51	2.05	2.44	[8]
Al_0.5CoCrFeMo_0.3Ni	FCC + BCC + IM	3325	814	1282	1529	31	4.08	2.59	2.17	1.88	[8]
Al_0.5CoCrFeMo_0.4Ni	FCC + BCC + IM	4286	1091	1664	1810	18	3.93	2.58	2.37	1.66	[8]
Al_0.5CoCrFeMo_0.5Ni	FCC + BCC + IM	5570	1544	-	2242	10	3.61	-	2.48	1.45	[8]
Al_0.5CoFeNiTi_0.5	FCC + BCC + IM	7188	-	-	2850	1.6	-	-	2.52	-	[90]
AlCrCuFeNi_0.6	FCC + BCC + IM	4848	1496	-	2025	2.87	3.24	-	2.39	1.35	[91]
AlCrCuFeNi	FCC + BCC + IM	4844	1496	-	1800	1.9	3.24	-	2.69	1.20	[91]
AlCrCuFeNi_1.2	FCC + BCC + IM	3998	1105	-	1298	1.4	3.62	-	3.08	1.17	[91]
AlCrCuFeNi_1.4	FCC + BCC + IM	3626	1265	-	1707	2.2	2.87	-	2.12	1.35	[91]

Phase	Tension			Compression
Phase	H_V/σ_y	H_V/σ_UTS		H_V/σ_yc	H_V/σ₁₀	H_V/σ_f
FCC	-	3 ± 0.29 ($\delta \ge 10\mathrm{\%}$)	-	-	3 ± 0.32 (${\varepsilon }_{\mathrm{f}}\ge 20\mathrm{\%}$)	-	-
BCC	3 ± 0.47 ($\delta \ge 10\mathrm{\%}$)	3 ± 0.27 ($\delta \ge 10\mathrm{\%}$)	≫3 ($\delta =0$)	3 ± 0.65(${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	3 ± 0.31 (${\varepsilon }_{\mathrm{f}}\ge 20\mathrm{\%}$)	3 ± 0.40 (${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	-
FCC + BCC	-	3 ± 0.23 ($\delta \ge 10\mathrm{\%}$)	> 3 ($\delta <10\%$)	-	3 ± 0.34 (${\varepsilon }_{\mathrm{f}}\ge 20\mathrm{\%}$)	3 ± 0.54 (${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	-
FCC + IM	-	-	> 3 ($\delta <10\%$)	-	3 ± 0.25 (${\varepsilon }_{\mathrm{f}}\ge 20\mathrm{\%}$)	3 ± 0.24 (${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	-
BCC + IM	-	-		3 ± 0.22 (${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	-	3 ± 0.33 (${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	> 3 (${\varepsilon }_{\mathrm{f}}=0$)
FCC + BCC + IM	-	-		3 ± 0.42 (${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	3 ± 0.44 (${\varepsilon }_{\mathrm{f}}\ge 20\mathrm{\%}$)	3 ± 0.54 (${\varepsilon }_{\mathrm{f}}<20\mathrm{\%}$)	-