Prakt. Met. Sonderband 46 (2014) 173
limensionless 4.2. EFFECT OF RESIDUAL STRESSES ON STRENGTH DISTRIBUTION
d material [7].
0.2 [5]: i Figure 4 represents the corresponding Weibull diagram, where the equivalent failure
igh-resolution stress, of, calculated for every specimen according to Eq. (3), is represented versus the
citation was probability of failure, F, for the LTCC_E, LTCC_T. TET_1 and TET_2 systems. It can be
-C specimens observed that the failure stress values in all cases Failure load, P [N]
nal from Cr follow a Weibull distribution, which is associated 10 16 23 29
alysed by the with the flaw size distribution in the sample. 99.94~ ~+2
or, Since the Although the presence of a threshold strength, cin
ortional to the ; . : ; — 93.40 1
; (Le. compressive stress) in the laminates would
S obiained by lead to a 3-paremeter Weibull distribution [11], w 63.21 23
ens made of this cannot be observed in Fig. 4. Thus, a 2- ¢ YR
measure on paremeter Weibull distribution, with op and m, was 2 30.78. 4%
scence. fit according to EN-843-5 [12]. The characteristic = = :
flexural strength and Weibull modulus for all = 12.66 a
samples tested, along with the calculated 90% ES g
confidence intervals, are given in Table 1. The © 4.86 -3
90% confidence interval represents the range 2 CCE
where the true Weibull parameters can be found % 18 oT f+
with a 90% probability. The effect on strength of 0.57 ‘hs
LTCC_E and compressive residual stresses at the surface of ‘ 150 250 350 450
sections were the TET_1 and TET 2 systems is clear. The Failure stress, o, [MPa]
3a), equiaxed combination of two bulk materials (i.e. LTCC_E _
ght-grey). For and LTCC_T) can lead to higher strengths in a Figure 4. Strength of LTCC bulk
-plane, as a multilayer architecture. The difference between Materials and laminate systems.
the strength of the laminate systems TET_1 and TET_2 and the strength of the LTCC_T
bulk material (set at the surface of the laminates) results (in average) in 60MPa and
80MPa, respectively. This difference in strength is in good agreement with the
compressive residual stresses estimated with Eq. (1) according to laminate theory, and is
also in agreement with the values measured with Raman spectroscopy.
Table 1. Weibull parameters (o, and m) of the strength distribution for LTCC_E, LTCC T,
TET_1 and TET_2 systems. The 90 % confidence intervals are given in brackets. Residual
stress calculated with Eq. (1) and measured with Raman are also listed.
LTCC Characteristic Weibull | Residual stress [MPa]
3 strength, modulus, Laminate theory | Raman measurements
ystem -
- — oo [MPa m [-] T |
5 um OT Laver OE Layer OT Layer OE Laver
zu
177 21
chris LICCE 474-1811 115-211 © J
226 33
) ppm/K and LTCCT 12237030) 21-475 °* ' A 5
ca. 0.6 ppm/K 286 26 i
ile i + +16 + -53 +
one ome TET 1 [282 — 290] [20 — 32] —44 +3 16 + 1 53+3
305 20 ;
TET2 00-3101 HM5-_241 —58+3 #311 -6641 -
-
:
3 r
m
