JP2765288B2 - Strength evaluation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

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

[0002]

2. Description of the Related Art A stress analysis using a finite element method has often been performed for evaluating the strength of a structure such as a semiconductor package. Quantitative strength evaluation can be performed from the maximum principal stress, equivalent stress, and the like obtained by inputting the material constant, shape, and constraint conditions.

However, unlike a metal material, a ceramic structure such as a ceramic package breaks due to minute cracks, so that it is difficult to quantitatively evaluate the strength with a maximum principal stress or equivalent stress. .

Conventionally, for such brittle materials,
In general, a method of evaluating the strength by a stress intensity factor at the tip of a crack is limited to cracks having a crack angle of 0 ° as shown in FIGS. 2 ( a ) to 2 ( c ).

In this field, the relationship between the crack size and the stress intensity factor has been investigated in detail for typical shapes and constraints of structures (Pergamon Pr).
"Stress Intensity F issued by ess
actors Handbook ").

Thus, the stress intensity factor, which is the strength of the stress field at the crack tip, can be calculated without performing the finite element analysis. By comparing this value with the fracture toughness value inherent to the material, a typical value is obtained. Evaluating the strength of structures having various shapes, constraint conditions and crack dimensions has been performed.

[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, for a structure such as a ceramic semiconductor package having many right-angled sharp grooves, the stress intensity factor cannot be calculated, 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 a stress analysis using the finite element method.

[0009]

In order to achieve the above object, a method for evaluating strength according to the present invention has a right-angle groove.
In the structure, the stress value around the groove is calculated by finite element analysis.
And calculate the stress intensity factor of each element using the stress value.
To predict the destruction of structures .

[0010] Further , the destruction conditions are determined for the stress intensity factors of the three deformation modes of the groove.

[0011]

[ Function ] "Strength Analysis I" (edited by Hiroyuki Okamura, pp100-
107, Ohmsha, '86 .9)
Generally, the stress intensity factor K at any point is

(Equation 1) (Where r is the distance from the crack tip to any point
Separation and σ are various responses based on the x-axis in FIGS. 2 (a) to 2 (c).
Force component, 1-λ is the stress singularity index)
K is ideally a constant value. Cracked crack
In the rack, 1−λ = 0.5. Also, stress at the tip
The following equation (Equation (1)) is used to derive the singular index. λ ₁ sin (2α) + sin (2αλ ₁ ) = 0 λ ₂ sin (2α) −sin (2αλ ₂ ) = 0 sin (2αλ ₃ ) = 0 where 2α is the angle surrounding the crack tip (the crack - shaped club ).
Α = 180 °).

FIG . 3 shows a ceramic structure having right-angle grooves.
Performs a 4-point bending test on the object, the groove radius of curvature and the breaking load
Is an experimental result 2 in which the relationship was examined.

Considering the curvature for each radius of curvature
Perform a finite element analysis and predict the fracture from the maximum principal stress value
The load 3 is also shown in FIG. In the experiment, the curvature of the groove was half
When the diameter is about several tens of μm, the breaking load does not decrease. This
It behaves like a crack with an opening angle of 0 °
is there. Therefore, a sharp groove with a radius of curvature of several tens of micrometers
Is equivalent to a crack with an opening angle of 0 °
You.

In the present invention, the ceramic structure is directly
The groove with a sharp corner is opened and treated as a crack having an angle of 90 °. Figure
2 (d) to (f) show three deformation modes of the right-angle groove.
is there. 1b is the tip of the groove. Crack place
Unlike the case, the crack propagation direction is the x-axis (= r direction),
The vertical direction within the same plane is defined as the y-axis, and the vertical direction outside the plane is defined as the z-axis.
Confuse.

In the case of a right-angle groove, α in the above equation (1)
Is α = (360 ° −90 °) / 2 = 135 °,
When the stress singularity index is derived, 1−λ ₁ = 0.456,
1−λ ₂ = 0.092 and 1−λ ₃ = 0.333.

Here, the stress intensity factor applied to the groove is expanded.
Called the tensile stress intensity factor,
The large coefficients are represented as K ₁ ′, K ₂ ′, and K ₃ ′, respectively. That is,
Expansion mode of each mode at a point in the direction of crack propagation
Force expansion coefficient is expressed as the following equation (Equation _{(2)) K 1 '=} σ y (2πr) 0.456 K 2' = τ xy (2πr) 0.092 K 3 '= τ yz (2πr) 0.333. Here, r is the crack propagation direction (x
(Axis), the distance from the tip (origin) 1b of the groove to a certain point, σ _y is the vertical stress component in the y direction in FIGS. 2 (d) to 2 (f) , and τ _xy is the Shear stress generation in xy plane
Min, tau _yz shear stress components in the yz plane of Fig. 2 (d) ~ (f)
It is.

Using the expanded stress intensity factor,
An example of strength evaluation of a structure having the same will be described step by step.
First, the crack propagation direction of the groove is defined as the x-axis (= r direction).
Then, finite element analysis is performed by applying a certain load.

For an element or node on the x-axis,
Min (σ _y , τ _xy , τ _yz ) and the distance r from the groove tip
You. By substituting these values into equation (2),
For each element or node, open, shift, and twist
The diffusion stress intensity factors K ₁ ′, K ₂ ′, and K ₃ ′ of the
It is.

Next, these expanded stress intensity factors are
Plotted against the distance r from. FIG. 1 shows each element.
This is an example in which K ₁ ′ is plotted. Near the tip of the groove
Since the value of K ₁ ′ includes a calculation error,
K ₁ ′ is obtained by a method such as extrapolating a straight line portion. like this
Then, K ₁ ′ at the tip of the groove under a certain load is calculated.
You.

For a simple load condition that breaks only in mode 1
In this case, this K ₁ ′ value becomes the material-specific fracture toughness value K _1c .
Destroy when it reaches. In addition, the value of K ₁ '
It is proportional to the applied load F0 during the limiting element analysis. Therefore,
The load Fb at which the destruction of the structure is predicted is Fb = F0x (K
_1c / K ₁ '). By this method,
Structure with right-angled grooves not possible with conventional
Can be quantitatively evaluated and predicted.

Furthermore, actual structures such as semiconductor packages
Has a complicated structure, and multiple deformation modes may occur.
In some cases, the groove may be broken at a right angle. This
In such cases, the material-specific fracture toughness value K _1c is used as the fracture condition.
Can not be used for
There is.

In claim 2 of the present invention, experiments and claims
Each of the grooves is based on the expanded stress intensity factor obtained in item 1.
Destruction conditions are defined for the deformation mode of. Then asked
3 modes for a structure that is small
, The expansion stress intensity factor is determined. The three models obtained
Express the stress expansion factor of the
And compare with destruction conditions. The resulting stress expansion
If the large coefficient is greater than the failure condition, the structure will break
It is expected.

By doing so, a structure having a groove portion
Breaks due to mixing of aperture, misalignment and torsion modes
In the case of a
It becomes possible to measure.

[0024]

Next, an embodiment of the present invention will be described with reference to FIG. 1 and FIGS.

Example 1 FIG. 4 shows the results of finite element analysis performed on a state in which a bending load is applied to a ceramic semiconductor package, and shows the maximum principal stress distribution near a right-angle groove having a radius of curvature of 10 μm. .

[0026] FIGS. 4 (a) was the maximum of the stress is the position of the groove portion destination end 1b shown in FIG. (B), the load weight 1
In the case of 0kgw, the maximum principal stress value is 121kg f / mm ²
Met. The fracture stress value of this ceramic material is 28 kg
an f / mm ^2, it is expected to break at 2.3kg f (= 10 × 28/ 121) if breakdown occurs when it reaches this value.

However, the breaking load in the experiment under the same conditions was 7.9 kgw. This is because, in the case of the ceramic structure, shows that by the conventional method of strength evaluation using the maximum principal stress occurring in sharp groove is impossible strength evaluation.

FIG. 1 shows an embodiment in which the stress intensity factor is applied to a right-angle groove. From the groove portion destination end 1b of FIG. 4, for each element arranged in the crack progress direction (r direction), we obtain the Figure 2 extended stress intensity factor K ₁ of mode 1 shown in (e) '.

K ₁ ′ is the stress component σ _y perpendicular to the r direction obtained from the finite element analysis result and the distance r from the groove tip 1 b to the center of each element is K ₁ ′ = σ _y (2πr) ^0.456 Was calculated. FIG. 1 plots this K ₁ ′ against r. By extrapolating the points of these linear portions, the expansion stress intensity factor at the groove tip 1b is obtained.
When K ₁ ′ is obtained , K ₁ ′ = 4.7 ^MPa · m ^0.456 .

The fracture toughness value K _1C inherent to this ceramic material
Is 3.83MPa√ (m), if destroyed when reaching this value occurs, 8.1kg f (= 10 ×
It is predicted to break at 3.83 / 4.7). This would have predicted accurately experimental value 7.9 kg f.

Table 1 shows a comparison between the method according to the first aspect of the present invention and the predicted value including the variation by the conventional method using the maximum principal stress. According to the first aspect of the present invention, the experimental value can be predicted with considerably better accuracy than the conventional method.

[0032]

[Table 1]

(Example 2) FIG. 5 shows an embodiment of claim 2 .
For the structure of the alumina material having a groove, the breaking conditions of each mode were determined . Experiments were performed on the opening, displacement, and torsion modes in the case of breaking in a single mode.
The destruction conditions of each mode were determined from the analysis of claim 1. The value of each mode is K _1C ′ = 3.2 MPa · m ^0.456 and K _2C ′ =
3.8 MPa · m ^0.092 , K ₃ ′ = 0.7 MPa · m
It was ^0.333 . 5 and illustrates the ellipsoid passing through the three points of this.

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 a support jig 5 as shown in FIG.
The breaking load in an experiment in which a load is applied by the load jig 6 is 99
was kg f.

An actual structure such as a semiconductor package is not necessarily broken in a single deformation mode. When this case is analyzed by the method of claim 1 of the present invention, 100
If you load the kgw, K ₁ '= 1.0MPa ·
m ^0.456 , K ₂ ′ = 0.1 MPa · m ^0.092 , K ₃ ′ = 0.
It was 63 MPa · m ^0.333 .

K ₁ ′ and K ₃ ′ are large, which means that the opening and the torsion mode occur simultaneously. In such cases, rather than evaluating as to destroy only the material-specific fracture toughness K _1C, the structure having a groove, FIG. 2
It is appropriate to evaluate the strength using FIG. 5 in which the destruction conditions of modes 1 to 3 of (a) to (c) are determined by experiments.

In the case of the PGA _{package, (K 1 '/ K 1C} ') 2 + (K 2 '/ K 2C') 2 + (K 3 '/
K _3C ') is a ² = 0.91 = 0.95 ^2. _{(K 1 '/ K 1C'} ) 2 + (K 2 '/ K 2C') 2 + (K 3 '/
If K _3C ') to break when ² = 1 ^2, breaking load to be predicted, 1
A 05kg f (= 100 × 1 / 0.95), which is consistent with the experimental values 99 kg f.

Thus, according to claim 2 of the present invention,
Even when a plurality of modes coexist, the experimental values can be predicted with fairly good accuracy.

(Example 3) FIG. 7 shows an experimental example in which a static load is applied to the structure 4b having a groove made of alumina.
Structure 4b, supported by the support jig 5, a load is applied by the load jig 6 in the center. The breaking load in the experiment was 7.1
was kg f. In this case, the analysis according to the method of claim 1 of the present invention shows that when a load of 10 kgf is applied.
K ₁ ′ = 2.8 MPa · m ^0.456 , K ₂ ′ = ^{3.0 MPa}
· M ^0.092, a ^{_{K 3 '= 0.53MPa · m 0.333}} .
Opening, shift, and all modes of torsion are _{mixed, (K 1 '/ K 1C} ') 2 + (K 2 '/ K 2C') 2 + (K 3 '/
K _3C ') is ² = 1.9 = 1.38 ^2.

The breaking load predicted by the method of claim 2 of the present invention, 7.3kg f (= 10 × 1 / 1.38)
, And the are match well with the experimental value 7.1kg f.

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

[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. This has the effect of quantitatively evaluating the strength of the structure.

[Brief description of the drawings]

1 is a diagram showing the relationship between the distance and the expansion stress intensity factor from the groove portion destination end.

Figure 2 (a) ~ (c) is a diagram showing three deformation modes and Crack coordinates crack, (d) ~ (f) is
It is a figure which shows the three deformation modes of a groove part, and the coordinate of a groove front-end | tip .

FIG. 3 is a diagram showing a relationship between a radius of curvature of a groove 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 a portion A in FIG. It is a figure showing a stress distribution.

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

FIG. 6A is a diagram showing a PGA semiconductor package ;
(B) is a diagram showing an experimental device for applying a static load to the PGA semiconductor 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 crack tip 1 b groove portion of the tip 2 Test Results 3 maximum stress due to the destruction predicted load 4a alumina semiconductor package 4b alumina structure 5 supporting jig 6 load jig

Claims (2)

(57) [Claims] 1. A structure having right-angle grooves, wherein the grooves
The stress value around the part is obtained by finite element analysis and the stress value
Calculate the stress intensity factor of each element using
A strength evaluation method characterized by predicting the strength. 2. Stress intensity factors for three deformation modes of a groove.
Strength evaluation method according to claim 1, characterized in that determining the breakdown condition for.