JPH0666696A - Strength evaluating method - Google Patents

Abstract

PURPOSE:To evaluate the strength of ceramic structure quantitatively by applying a stress intensity factor to a right angle groove part and determining critical fracture values of stress intensity factor for three deformation modes at the groove part. CONSTITUTION:A sharp right angle groove part of ceramic structure is recognized as a crack having open angle of 90 deg. and four point bending test is performed to determine the relationship between the radius of curvature at groove part and fracture load. Experimental values 2 do not match with fracture load 3 predicted through finite element analysis and the radius of curvature of several tens mum corresponds to crack having open angle of 0 deg.. When a sharp right angle groove is treated as a chappy crack, extended stress intensity factors K' corresponding to three modes, opening, shift, and tear are determined as follows; K'1=sigmay(2pir)<0.45>, K'2=tauxy(2pir)<0.09>, K'3=tau(2pir)<0.33>, where sigma: stress, tau: shearing stress, r: distance from the tip of groove. The extended stress intensity factors K' thus determined represent critical fracture values inherent to the structure and thereby the strength can be quantified.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a strength evaluation method using a stress intensity factor.

[0002]

2. Description of the Related Art Stress analysis using a finite element method has often been performed for strength evaluation of structures such as semiconductor packages. Quantitative strength evaluation can be performed from the maximum principal stress, equivalent stress, etc. obtained by inputting material constants, shapes, and constraint conditions.

However, unlike a metal material, a ceramic structure such as a ceramic package is broken due to minute cracks, and thus quantitative strength evaluation is difficult with maximum principal stress or equivalent stress. .

Conventionally, for such brittle materials,
Generally, a method of evaluating the strength by the stress intensity factor at the tip of the crack is generally used only for the cracked crack having an opening angle of 0 ° as shown in FIGS. 2B to 2D.

In this field, the relation between the crack size and the stress intensity factor has been investigated in detail for the typical shape and restraint conditions of a structure (Pergamon Pr.
Ess's "Strength Integrity F"
actors Handbook ”etc.).

This makes it possible to calculate the stress intensity factor, which is the strength of the stress field at the crack tip, without performing finite element analysis. By comparing this value with the fracture toughness value peculiar to the material, a typical It has been performed to evaluate the strength of structures with various shapes, restraint conditions and crack sizes.

[0007]

However, the conventional method can be applied only to a crack having an opening angle of 0 ° and cannot be applied to a sharp groove having an opening angle of 90 °. For this reason, the stress intensity factor cannot be calculated for a structure having many right-angled sharp grooves such as a ceramic semiconductor package, and therefore the strength of the structure cannot be evaluated in comparison with the fracture toughness value. There was a point.

An object of the present invention is to provide a method for quantitatively evaluating the strength of a structure in stress analysis using the finite element method.

[0009]

In order to achieve the above object, in the strength evaluation method according to the present invention, in the stress analysis using the finite element method, the stress intensity factor is applied to the right-angled groove portion of the structure. The strength is quantitatively evaluated.

Further, the critical fracture value of the stress intensity factor is determined for the three deformation modes of the groove.

[0011]

According to the first aspect of the present invention, the right-angled sharp groove portion of the ceramic structure is treated as a crack having an opening angle of 90 °. FIG. 3 shows an experimental result 2 in which a four-point bending test was performed on a ceramic structure having a right-angled groove portion, and the relationship between the groove radius of curvature and the fracture load was investigated.

For each radius of curvature, finite element analysis was performed considering the curvature, and the fracture load 3 predicted from the maximum principal stress value is also shown in the same figure. In the experiment, the fracture load does not decrease when the radius of curvature of the groove is about several tens of μm. This is a behavior similar to a crack having an opening angle of 0 °.

Therefore, it can be said that a sharp groove having a radius of curvature of several tens of μm is equivalent to a crack having a crack with an opening angle of 0 °. Generally, the stress intensity factor K is K = σ (2πr) ⁻⁰ · ⁶ ρ: stress value, r: the strength of the stress field defined by the distance from the groove tip, and ideally K is a constant value. . This is applied to the right-angled groove.

2 (a)-(d) show three deformation modes of the crack and also a groove at right angles with coordinate axes. In the present invention, the radius of curvature as shown in FIG.
A right-angled sharp groove (crack with an opening angle of 90 °) of about m is treated in the same manner as a crack-like crack as shown in (a) to (c). 1 indicates the tip of the groove crack. In the case of this groove crack, when deriving parameters specific to the stress at the tip, [λ ₁ sin (2α) + sin (2αλ ₁ )] · [λ ₂ sin (2α) −sin (2αλ ₂ )] · sin (2αλ ₃ ) = 0 by solving K _I '= σ _y (2πr) ⁻⁰ · ⁴⁵⁵⁵ ... Mode I (a) σ _y : vertical stress component in the y direction in FIG. 2 K _II ' = τ _xy (2πr) ^{− 0} - ⁰⁹¹⁵ ... mode II (b) τ
_xy: Shear stress components in the xy plane _{K III '= τ yz (2πr} ) -0 · 3333 ... mode III (c)
τ _yz : It can be expressed as a shear stress component in the yz plane.

The stress intensity factor applied to the groove portion in this manner is referred to as an extended stress intensity factor, and is referred to as a mode I, II, I.
The extended stress intensity factors of II are K _I ', K _II ' and K _III ', respectively.
Express.

An example in which the strength of the structure is evaluated from the expanded stress intensity factor, which is the stress field at the tip of the groove, will be described step by step. First, a finite element analysis is performed by applying a certain load, and the direction perpendicular to the maximum principal stress direction of the groove is defined as the r direction.

The stress values (σ _y , τ _xy , τ _yz ) of the element or node in that direction are calculated together with the distance r from the tip of the groove. By substituting these values into the above equations for calculating K _I ', K _II ' and K _III ', the K'value of each mode (aperture, shift, tear) is calculated for each element (node). It

Next, these K'values are calculated as the distance r from the groove tip.
Plot against. FIG. 1 is an example in which K _I 'of each element is plotted. K _I 'at the tip of the groove portion under a certain load is obtained by a method such as extrapolating these straight portions.

Conventionally, a stress intensity factor limited to a crack having an opening angle of 0 ° is applied to such a right-angled groove. The K _I 'value thus obtained is proportional to the load applied during the finite element analysis. Therefore, the load at which this K _I 'value reaches the fracture toughness value K _IC peculiar to the material is set as the fracture prediction load of the ceramic structure.

By using such a method, it is possible to quantitatively evaluate the strength of a ceramic structure having a right-angled groove portion, which has hitherto been impossible. Further, an actual structure such as a semiconductor package has a complicated shape and may be destroyed in a plurality of deformation modes.

In the second aspect of the present invention, the pseudo fracture toughness value is determined for the three deformation modes of the groove portion from the experiment and the analysis of the first aspect. This is obtained by measuring a fracture load value in each deformation mode in an experiment using a structure having a right-angled groove portion and using it for finite element analysis.

Since the stress intensity factor is proportional to the load applied during the finite element analysis, the stress intensity factor thus obtained represents a critical fracture value or pseudo fracture toughness value peculiar to a structure having a right-angled groove.

By doing so, when the structure having the groove portion is broken in any of the modes of opening, shifting and tearing shown in FIGS. 2A to 2D, the strength is quantitatively evaluated. It becomes possible to predict.

[0024]

EXAMPLE An example of the present invention will be described below with reference to FIGS. 1 and 4 to 8.

(Example 1) FIG. 4 is a finite element analysis result performed on a ceramic semiconductor package under a bending load, showing the maximum principal stress distribution in the vicinity of a right-angled groove having a radius of curvature of 10 μm. .

The maximum stress is shown in FIG. 4 (a) at the position of the groove crack tip 1 shown in FIG. 4 (b). When the load weight is 10 kgw, the maximum principal stress value is 121 kgw /
It was mm ² . The fracture stress value of this ceramic material is 2
It is 8 kgw / mm ² , and if the destruction occurs when this value is reached 2.3 kgw (= 10 × 28/121)
It is expected to be destroyed in.

However, the breaking load in the experiment under the same conditions was 7.9 kgw. This indicates that in the case of a ceramic structure, strength evaluation cannot be performed by the conventional method of strength evaluation using the maximum principal stress generated in a sharp groove.

FIG. 1 is an embodiment of claim 1 in which the stress intensity factor is applied to a groove having a right angle. Mode I shown in FIG. 2A for each element arranged in the r direction (crack propagation direction) perpendicular to the groove surface from the groove crack tip 1 in FIG.
The expansion stress intensity factor K _I 'of is calculated.

K _I 'is the stress component σ _y perpendicular to the r direction obtained from the above finite element analysis result and the distance r from the tip 1 to the center of each element K _I ' = σ _y (2πr) ^-0 Calculated by substituting for ⁴⁵⁵⁵ . This K _I 'is plotted against r in FIG. By extrapolating these straight line points, the expansion stress intensity factor K at the crack tip 1
_When I'is obtained, K _I '= 4.7 MPa√ (m).

Fracture toughness value K _IC peculiar to this ceramic material
Is 3.83 MPa√ (m), and if a fracture occurs when this value is reached, 8.1 kgw (= 10 × 3.
83 / 4.7). This means that the experimental value of 7.9 kgw is accurately predicted.

Table 1 is a comparison of the predicted values of the method according to claim 1 of the present invention and the conventional method using the maximum principal stress, including variations. According to claim 1 of the present invention, the experimental value can be predicted with considerably good accuracy as compared with the conventional method.

[0032]

[Table 1]

(Example 2) FIG. 5 is an embodiment of claim 2 in which the pseudo fracture toughness value of each mode is determined for a structure made of an alumina material having a groove. With respect to the opening, displacement, and tear modes, experiments were carried out in the case of fracture in a single mode, and the pseudo fracture toughness value of each mode was obtained from the analysis of claim 1. The value of each mode is K _IC '= 3.2 MPa√ (m), K
_IIC '= 3.8 MPa√ (m), K _IIIC ' = 0.7MP
It was a√ (m). FIG. 5 further depicts an elliptical surface that passes through these three points.

FIG. 6 shows an experimental example in which a static load is applied to the PGA semiconductor package 4a shown in FIG. This package is made of the same alumina material as in FIG. 5, and is supported on the support jig 5 as shown in FIG. 6 (b).
The breaking load in the experiment in which the load is applied by the loading jig 6 is 99.
It was kgw.

Actual structures such as semiconductor packages do not always break in a single deformation mode. In this case, the analysis according to the method of claim 1 of the present invention yields 100
When kgw is loaded, K _I '= 1.0 MPa√
(M), K _II '= 0.1 MPa√ (m), K _III ' =
It was 0.63 MPa√ (m).

Since K _I 'and K _III ' are large, it means that the opening and tearing modes are occurring at the same time. In such a case, the fracture toughness value K _IC peculiar to the material is not evaluated as the fracture, and the structure having the groove is not evaluated.
It is appropriate to evaluate the strength of the pseudo fracture toughness values of Modes I to III of (a) to (c) using FIG.

In the case of the PGA package, (K _I '/ K _IC ') ² + (K _II '/ K _IIC ') ² +
_{(K III '/ K IIIC'} ) is a ² = 0.91 = 0.95 ^2. (K _I '/ K _IC ') ² + (K _II '/ K _IIC ') ² +
If _{(K III '/ K IIIC'} ) destroyed when ² = 1 ² occurs, breaking load is predicted,
105 kgw (= 100 × 1 / 0.95), which is in good agreement with the experimental value of 99 kgw.

Thus, according to claim 2 of the present invention,
Even when a plurality of modes are mixed, the experimental value can be predicted with considerably good accuracy.

Example 3 FIG. 7 shows an experimental example in which a static load is applied to the above-mentioned structure 4b having a groove portion made of alumina.
The structure 4b is supported by the support jigs 5 and 5, and the load of the load jig 6 is applied to the center. The breaking load in the experiment is 7.1.
It was kgw. When this case is analyzed by the method of claim 1 of the present invention, K _I '= 2.8 MPa√ (m), K _II ' = 3.0 MPa when 10 kgw is loaded.
√ (m), K _III ′ = 0.53 MPa √ (m).
All modes of aperture, shift, and tear are mixed, and (K _I '/ K _IC ') ² + (K _II '/ K _IIC ') ² +
_{(K III '/ K IIIC'} ) is a ² = 1.9 = 1.38 ^2.

The breaking load predicted by the method of claim 2 of the present invention is 7.3 kgw (= 10 × 1 / 1.38).
Which is in good agreement with the experimental value of 7.1 kgw.

As described above, according to the first and second aspects of the present invention, even when a plurality of modes are mixed, it is possible to quantitatively evaluate and predict the intensity thereof.

[0042]

As described above, according to the present invention, the stress intensity factor is applied to the groove at a right angle based on the stress value obtained by the finite element analysis. It has the effect of quantitatively evaluating the strength of the structure.

[Brief description of drawings]

FIG. 1 is a diagram showing a relationship between a distance from a tip of a groove crack and an expansion stress intensity factor.

2A to 2D are diagrams showing three deformation modes of a crack and coordinates of a crack in a groove portion at right angles.

FIG. 3 is a diagram showing a relationship between a radius of curvature of a groove portion and a breaking load.

4A is a diagram showing a state in which a bending load is applied to the ceramic semiconductor package, and FIG. 4B is an enlarged view of an A portion of FIG. 4A, showing a maximum main portion near a right-angled groove portion having a curvature radius of 10 μm. It is a figure which shows stress distribution.

FIG. 5 is a diagram for obtaining a pseudo fracture toughness value in each mode for a structure made of an alumina material having a groove.

6A is a diagram showing a PGA semiconductor package, and FIG. 6B is a diagram showing an experimental apparatus for applying a static load to this package.

FIG. 7 is a diagram showing an experimental example in which a static load is applied to a structure having a groove made of alumina.

[Explanation of symbols] 1 tip of groove crack 2 experimental result 3 predicted fracture load due to maximum principal stress 4a alumina semiconductor package 4b structure made of alumina 5 support jig 6 load jig

[Procedure amendment]

[Submission date] July 19, 1993

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Figure 6

[Correction method] Change

[Correction content]

FIG. 6 is a diagram showing a PGA semiconductor package and an experimental apparatus for applying a static load to the package.

Claims (2)

[Claims] 1. In stress analysis using the finite element method,
A strength evaluation method characterized in that the strength of a structure is quantitatively evaluated by applying a stress intensity factor to a groove at a right angle. 2. The fracture critical value of the stress intensity factor is determined for three deformation modes of the groove.
The strength evaluation method described in.