JP2008209262A - Quick evaluation method of elasticity, plasticity, and creep characteristic - Google Patents
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本発明は、弾・塑性・クリープ特性評価を、瞬間的負荷部とひずみ保持部から成る1種類の階段波負荷試験のみで実行可能とする弾・塑性・クリープ特性の迅速評価方法に関する。 The present invention relates to a rapid evaluation method for elastic / plastic / creep characteristics, which makes it possible to perform an elastic / plastic / creep characteristic evaluation by only one type of staircase load test composed of an instantaneous load section and a strain holding section.
従来、計算コストの削減のために、弾・塑性有限要素解析のみに因っていた機器の設計分野においても、弾・塑性・クリープ有限要素解析が実行される機会が増えてきている。 これは、クリープ変形が生じる部位の存在が予測される機器に対して、より高い安全性が要求されるようになった為である。
また、計算技術の発展により、弾・塑性・クリープ有限要素解析が従来に比べ短時間で実行できるようになったこともその一因と考えられる。
弾・塑性・クリープ有限要素解析を実行するためには、解析対象となる材料の弾・塑性・クリープ特性を調査し、その特性を反映させた材料定数を決定しなければならない。
これらの材料定数は、数種類のひずみ速度による引張試験と数種類の保持応力によるクリープ試験から決定する必要がある。
また、変形特性の温度依存性を考慮する際には、これらの試験は複数の温度下で実行しなければならず、弾・塑性・クリープ有限要素解析の実施までには、さらに多くの試験の実施が不可欠となる。
特に、クリープ試験は長時間におよぶことが多いため、このような試験を多数実施することは、材料定数を決定し弾・塑性・クリープ有限要素解析を実施するまでに膨大な時間を要することを意味する。
すなわち、計算技術の発展により弾・塑性・クリープ解析を如何に高速で実行できるようになっても、解析を実行するまでのクリープ試験時間を短縮できなければ、弾・塑性・クリープ解析を実行するためのハードルは依然高いままである。
以上のことから、材料の弾・塑性・クリープ特性を極少数の実験から速やかに評価し、この特性を反映した材料定数を的確に導出できる弾・塑性・クリープ特性の迅速評価方法の構築が望まれている。
Conventionally, in order to reduce the calculation cost, the opportunity for executing the elastic / plastic / creep finite element analysis is increasing also in the field of equipment design, which is based solely on the elastic / plastic finite element analysis. This is because a higher level of safety is required for a device that is predicted to have a site where creep deformation occurs.
Another reason is that the advancement of computational technology has made it possible to perform elastic / plastic / creep finite element analysis in a shorter time than before.
In order to perform elastic / plastic / creep finite element analysis, it is necessary to investigate the elastic / plastic / creep characteristics of the material to be analyzed and to determine the material constants that reflect the characteristics.
These material constants need to be determined from tensile tests with several strain rates and creep tests with several holding stresses.
In addition, when considering the temperature dependence of deformation characteristics, these tests must be performed at multiple temperatures, and many more tests are required before conducting an elasto-plastic-creep finite element analysis. Implementation is essential.
In particular, the creep test often takes a long time, so performing many such tests requires enormous amounts of time to determine the material constants and perform the elastic / plastic / creep finite element analysis. means.
In other words, even if it becomes possible to execute elastic / plastic / creep analysis at high speed due to the development of calculation technology, if the creep test time until analysis is not shortened, elastic / plastic / creep analysis is executed. The hurdles to remain remain high.
Based on the above, it is hoped that a rapid evaluation method for elastic, plastic, and creep properties that can quickly evaluate the elastic, plastic, and creep properties of materials from very few experiments and accurately derive material constants that reflect these properties is hoped for. It is rare.
なお、公知技術として、IC(集積回路)チップをプリント基板に実装したICパッケージなどの電子機器において、寿命サイクル数を簡単で正確に求めて、信頼性をより簡単で正確に評価できる電子機器の信頼性評価方法及びその信頼性評価装置が知られている(特許文献1を参照)。
この公知技術は、特定の電子機器に対する周期的温度条件下にさらす加速試験、すなわち温度サイクル試験を行って、全ての電気機器に普遍な寿命サイクル数と歪み振幅との関係式、すなわち寿命歪み関係式を求め、任意の電子機器の解析モデルに対して熱応力シミュレーションを行い、歪みの振幅を算出し、次に寿命歪み関係式に、任意の電子機器の解析モデルに対する歪み振幅を代入して、任意の電子機器の解析モデルの寿命サイクル数を求めるものである。
In addition, as a publicly known technique, in an electronic device such as an IC package in which an IC (integrated circuit) chip is mounted on a printed circuit board, an electronic device that can easily and accurately evaluate reliability by obtaining the number of life cycles easily and accurately. A reliability evaluation method and a reliability evaluation apparatus thereof are known (see Patent Document 1).
This known technology performs an accelerated test that is exposed to a periodic temperature condition for a specific electronic device, that is, a temperature cycle test, and a universal relationship between the number of life cycles and strain amplitude for all electrical devices, that is, a life strain relationship. Obtain the equation, perform thermal stress simulation on the analysis model of any electronic device, calculate the strain amplitude, and then substitute the strain amplitude for the analysis model of any electronic device into the lifetime strain relational expression, The life cycle number of an analysis model of an arbitrary electronic device is obtained.
本発明は、従来は数種類のひずみ速度下での引張試験と数種類の保持応力でのクリープ試験を実施しなければならなかった弾・塑性・クリープ特性評価を、瞬間的負荷部とひずみ保持部から成る1種類の階段波負荷試験のみで実行可能とする弾・塑性・クリープ特性の迅速評価方法を提供することを目的とする。 In the present invention, an elastic, plastic, and creep property evaluation that has conventionally had to be carried out with a tensile test under several strain rates and a creep test with several holding stresses was performed from an instantaneous load section and a strain holding section. An object of the present invention is to provide a rapid evaluation method for elastic, plastic, and creep characteristics that can be executed only by one type of staircase load test.
本発明の弾・塑性・クリープ特性の迅速評価方法は、瞬間的負荷とひずみ保持を繰返す階段波負荷試験を実施し、瞬間的負荷部に対応する応力−ひずみ曲線から応力‐弾塑性ひずみ曲線を取得する第一工程と、前記応力−弾塑性ひずみ曲線から弾・塑性特性に関する材料定数を導出する第二工程と、応力緩和曲線から、応力とクリープひずみ速度の関係を取得する第三工程と、繰返し応力緩和曲線から,遷移クリープひずみ速度と定常クリープひずみ速度の比を取得する第四工程と、前記第三工程及び第四工程で得た情報から、定常クリープ則と遷移クリープ則の材料定数を導出する第五工程とを含むものである。 The rapid evaluation method for elastic / plastic / creep characteristics of the present invention performs a step wave load test that repeats instantaneous load and strain retention, and calculates a stress-elasto-plastic strain curve from the stress-strain curve corresponding to the instantaneous load part. A first step of acquiring, a second step of deriving a material constant relating to elastic / plastic properties from the stress-elastic-plastic strain curve, a third step of acquiring a relationship between stress and creep strain rate from the stress relaxation curve, From the fourth step of obtaining the ratio of the transition creep strain rate to the steady creep strain rate from the cyclic stress relaxation curve, and the information obtained in the third step and the fourth step, the material constants of the steady creep law and the transition creep law are obtained. And a fifth step to be derived.
前記第一工程では、階段波負荷の全ての瞬間的負荷から弾塑性変形部のみを抽出し、これらをつなぎ合わせることで、弾・塑性特性の評価に必要な応力‐弾・塑性ひずみ曲線を取得するものである。 In the first step, only the elasto-plastic deformation part is extracted from all the instantaneous loads of the staircase wave load, and these are connected to obtain the stress-elastic-plastic strain curve necessary for evaluating the elasto-plastic characteristics. To do.
前記第二工程では、弾・塑性特性を表す材料定数のヤング率と塑性接線係数は応力‐弾塑性ひずみ関係から取得するものである。 In the second step, the Young's modulus and the plastic tangent coefficient of the material constant representing the elastic / plastic characteristics are obtained from the stress-elastic-plastic strain relationship.
前記第三工程では、応力緩和曲線から得た応力と応力速度の関係から、クリープ特性を評価するために不可欠となる応力とクリープひずみ速度の関係を取得するものである。 In the third step, the relationship between stress and creep strain rate, which is indispensable for evaluating creep characteristics, is obtained from the relationship between stress and stress rate obtained from the stress relaxation curve.
前記第四工程では、応力緩和曲線を前記第三工程に適用して、応力とクリープひずみ速度の関係を取得し、繰返し応力緩和曲線を構成する複数の応力緩和曲線に前記第三工程を適用し、各応力緩和曲線の応力とクリープひずみ速度の関係を取得し、取得した複数の応力緩和曲線でのクリープひずみ速度中の定常クリープひずみ速度を算出し、前記クリープひずみ速度と前記定常クリープひずみ速度の差から、遷移クリープひずみ速度を算出し、算出した定常クリープひずみ速度と遷移クリープひずみ速度を用いて、遷移クリープひずみ速度と定常クリープひずみ速度の比を算出するものである。 In the fourth step, a stress relaxation curve is applied to the third step, the relationship between stress and creep strain rate is obtained, and the third step is applied to a plurality of stress relaxation curves constituting the repeated stress relaxation curve. The relationship between the stress of each stress relaxation curve and the creep strain rate is obtained, the steady creep strain rate is calculated during the creep strain rate of the obtained plurality of stress relaxation curves, and the creep strain rate and the steady creep strain rate are calculated. The transition creep strain rate is calculated from the difference, and the ratio between the transition creep strain rate and the steady creep strain rate is calculated using the calculated steady creep strain rate and transition creep strain rate.
本発明の弾・塑性・クリープ特性の迅速評価方法は、材料の弾・塑性・クリープ特性を極少数の実験から速やかに評価し、この特性を反映した材料定数を的確に導出することができる。 The rapid evaluation method of elastic / plastic / creep characteristics of the present invention can quickly evaluate the elastic / plastic / creep characteristics of a material from a very small number of experiments and accurately derive a material constant reflecting the characteristics.
本発明の弾・塑性・クリープ特性の迅速評価方法の一実施例を図面に基づいて、以下に説明する。
図1は、本発明の弾・塑性・クリープ特性の迅速評価方法の階段波負荷試験の概念摸式図を示す。
図1では、階段波負荷試験のIS部が瞬間的負荷部、MS部がひずみ保持部に相当する。
IS部ではひずみ増分Δεisが瞬間的に与えられるため、そこに対応する応力−ひずみ関係ではクリープの影響が排除される。
MS部では応力緩和が生じる。
また、この階段波負荷試験では、ひずみεendに到達したらΔtendの間、ひずみεendを保持し、MS部よりも長い時間に渡る応力緩和曲線を取得する。
表1に階段波負荷試験条件の例、εend=4.4×10−2、Δtend=600sec、を示す。
One embodiment of the rapid evaluation method for elastic / plastic / creep characteristics of the present invention will be described below with reference to the drawings.
FIG. 1 is a conceptual model diagram of a staircase wave load test of the rapid evaluation method for elastic / plastic / creep characteristics of the present invention.
In FIG. 1, the IS part of the staircase load test corresponds to the instantaneous load part, and the MS part corresponds to the strain holding part.
In the IS part, since the strain increment Δε is is given instantaneously, the influence of creep is eliminated in the corresponding stress-strain relationship.
Stress relaxation occurs in the MS part.
In this step wave load test, when the strain ε end is reached, the strain ε end is held for Δt end and a stress relaxation curve is acquired over a longer time than the MS portion.
Table 1 shows examples of staircase wave load test conditions, ε end = 4.4 × 10 −2 , Δt end = 600 sec.
図2は、階段波負荷試験で得られる応力−ひずみ曲線である。
図2の丸印で示す初期部での応力の増減は、図3の繰返し応力緩和曲線のように瞬間的負荷による応力の増加とひずみ保持による応力緩和が繰返し生じることに起因する。
また、丸印で示す終端部での応力の低下は、ひずみεendでΔtend間ひずみを保持したことで生じる図4の応力緩和曲線のように応力緩和に起因する。
FIG. 2 is a stress-strain curve obtained in a step wave load test.
The increase / decrease in stress at the initial portion indicated by a circle in FIG. 2 is caused by repeated increase in stress due to instantaneous load and stress relaxation due to strain retention as shown in the repeated stress relaxation curve in FIG.
Further, the decrease in stress at the terminal end indicated by a circle is caused by stress relaxation as shown in the stress relaxation curve of FIG. 4 generated by holding the strain during Δt end with strain ε end .
本発明では、図2の応力−ひずみ曲線と図3、図4の応力緩和曲線を、以下の5つの技術に適用することで弾・塑性・クリープ特性を評価する。
(1)瞬間的負荷部に対応する応力−ひずみ曲線から応力−弾塑性ひずみ曲線を取得する技術。
(2)前記応力−弾塑性ひずみ曲線から、弾・塑性特性に関する材料定数を導出する技術。
(3)応力緩和曲線から、応力とクリープひずみ速度の関係を取得する技術。
(4)繰返し応力緩和曲線から、遷移クリープひずみ速度と定常クリープひずみ速度の比を取得する技術。
(5)上記(3)、(4)で得た情報から、定常クリープ則と遷移クリープ則の材料定数を導出する技術。
上記5つの技術の詳細は,以下の通りである。
In the present invention, the elastic-plastic / creep characteristics are evaluated by applying the stress-strain curve of FIG. 2 and the stress relaxation curves of FIGS. 3 and 4 to the following five techniques.
(1) A technique for obtaining a stress-elasto-plastic strain curve from a stress-strain curve corresponding to an instantaneous load portion.
(2) A technique for deriving material constants relating to elastic / plastic properties from the stress-elastic-plastic strain curve.
(3) Technology for obtaining the relationship between stress and creep strain rate from a stress relaxation curve.
(4) A technique for obtaining a ratio between a transition creep strain rate and a steady creep strain rate from a cyclic stress relaxation curve.
(5) A technique for deriving the material constants of the steady creep law and the transition creep law from the information obtained in (3) and (4) above.
The details of the above five techniques are as follows.
図6の丸印で示す曲線は、この処理を図2の応力−ひずみ曲線に適用して取得した応力−弾塑性ひずみ曲線に相当する。 A curve indicated by a circle in FIG. 6 corresponds to a stress-elastic-plastic strain curve obtained by applying this process to the stress-strain curve of FIG.
(2)の技術:弾・塑性特性を表す材料定数のヤング率と塑性接線係数は応力−弾塑性ひずみ関係から取得する。
特に、塑性接線係数は、応力あるいはひずみの関数として取得すれば、正確な変形シミュレーションが可能となる。
本技術では、図6で得た応力−弾・塑性ひずみ曲線を、弾性ひずみと塑性ひずみの和で弾・塑性ひずみを表すRamberg-Osgood則で図7のように応力−弾・塑性ひずみ曲線を近似する。
Ramberg-Osgood則は、数1の形で与えられる。
Technique (2): The Young's modulus and plastic tangent coefficient of material constants representing elastic / plastic properties are obtained from the stress-elasto-plastic strain relationship.
In particular, if the plastic tangent coefficient is acquired as a function of stress or strain, an accurate deformation simulation is possible.
In this technology, the stress-elastic / plastic strain curve obtained in FIG. 6 is expressed by the Ramberg-Osgood law, which represents the elastic-plastic strain as the sum of elastic strain and plastic strain, as shown in FIG. Approximate.
The Ramberg-Osgood law is given in the form of
また、右辺第1、2項目は、それぞれ弾性ひずみと塑性ひずみに相当する。
したがって、応力と塑性ひずみの関係を表す塑性接線係数Hは、右辺第2項目を微分すれば、数2のように応力の関数として得られる。
The first and second items on the right side correspond to elastic strain and plastic strain, respectively.
Therefore, the plastic tangent coefficient H representing the relationship between the stress and the plastic strain can be obtained as a function of the stress as shown in Equation 2 by differentiating the second item on the right side.
Ramberg-Osgood則による近似処理は以下の順で行う。
(i) 応力とひずみが線形関係にある低応力域で、応力とひずみの関係を直線近似してヤング率Eを決定する。
(ii) 基準塑性ひずみを適当に設定し(図7の近似ではε0=5.0×10-4)、対応する基準応力Dを決定する。
(iii) (i),(ii)で決定したEとDの値と、応力−弾・塑性ひずみ曲線の任意の点における応力とひずみの値を用いて硬化指数mを算出する。
以上のRamberg-Osgood則による近似処理を通じ、ヤング率や塑性接線係数が取得できる。
The approximation process by the Ramberg-Osgood rule is performed in the following order.
(i) The Young's modulus E is determined by linearly approximating the relationship between stress and strain in a low stress region where the stress and strain are in a linear relationship.
(ii) The reference plastic strain is set appropriately (ε 0 = 5.0 × 10 −4 in the approximation of FIG. 7), and the corresponding reference stress D is determined.
(iii) The hardening index m is calculated using the values of E and D determined in (i) and (ii) and the stress and strain values at arbitrary points on the stress-elastic / plastic strain curve.
The Young's modulus and plastic tangent coefficient can be obtained through the approximation process based on the above Ramberg-Osgood rule.
(3)の技術:ひずみ保持による応力緩和では、クリープひずみの増加量と弾性ひずみの減少量が釣り合った状態にある。
本技術では、このことに着目し、応力緩和曲線から得た「応力と応力速度の関係」から、クリープ特性を評価するために不可欠となる「応力とクリープひずみ速度の関係」を取得する。
「応力と応力速度の関係」は、応力緩和曲線上の複数の点で、図8のように接線の傾きから応力速度を算出して取得する。
算出した応力速度は、数3の応力速度とクリープひずみ速度の関係に適用する。
Technique (3): In stress relaxation by strain retention, the amount of increase in creep strain is balanced with the amount of decrease in elastic strain.
In this technology, paying attention to this, the “relationship between stress and creep strain rate” which is indispensable for evaluating the creep characteristics is obtained from the “relationship between stress and stress rate” obtained from the stress relaxation curve.
The “relationship between stress and stress rate” is obtained by calculating the stress rate from the slope of the tangent as shown in FIG. 8 at a plurality of points on the stress relaxation curve.
The calculated stress rate is applied to the relationship between the stress rate of
応力緩和曲線上の複数の応力点で取得した応力速度を数3に適用すれば、「応力とクリープひずみ速度の関係」が得られる。
If the stress rates acquired at a plurality of stress points on the stress relaxation curve are applied to
また、遷移クリープひずみ速度は数5のように、定常クリープひずみ速度に比例する型で与える。
The transition creep strain rate is given by a type proportional to the steady creep strain rate, as shown in
数5の比例係数C1は、遷移クリープひずみが発達するとゼロとなる関数として、数6で表す。
The proportionality coefficient C 1 in
(4)の技術は、数5、数6を定式化するために必要となる「遷移クリープひずみ速度と定常クリープひずみ速度の比」を取得するためのものである。
「遷移クリープひずみ速度と定常クリープひずみ速度の比」は、以下の手順で取得する。
The technique (4) is for obtaining the “ratio between the transition creep strain rate and the steady creep strain rate” necessary for formulating the equations (5) and (6).
The “ratio between the transition creep strain rate and the steady creep strain rate” is obtained by the following procedure.
(i) ひずみεendでΔtend間ひずみを保持すること(図1、2参照)で得られる応力緩和曲線では、クリープひずみが十分に発達しているため、クリープ変形は定常クリープのみで生じる。
そこで、ここで得られる応力緩和曲線を(3)の技術に適用して、「応力とクリープひずみ速度の関係」を取得する。
そして、この関係を図9のようにプロットして、この関係の近似曲線から、定常クリープ則を定式化する。
図9では、定常クリープ則として数7のNorton則を用いた。
(i) the strain epsilon end The by holding the strain between Delta] t end The in stress relaxation curve obtained in (see FIGS. 1 and 2), since the creep strain is fully developed, creep deformation occurs only in the steady creep.
Therefore, the stress relaxation curve obtained here is applied to the technique (3) to obtain the “relationship between stress and creep strain rate”.
Then, this relationship is plotted as shown in FIG. 9, and a steady creep law is formulated from the approximate curve of this relationship.
In FIG. 9, the Norton law of Formula 7 is used as the steady creep law.
(iv) (iii)で算出した定常クリープひずみ速度と遷移クリープひずみ速度を用いて、「遷移クリープひずみ速度と定常クリープひずみ速度の比」を算出する。 (iv) Using the steady creep strain rate and the transition creep strain rate calculated in (iii), calculate the “ratio between the transition creep strain rate and the steady creep strain rate”.
(5)の技術:定常クリープ則の材料定数は、(4)の技術の手順(i)により決定する。
遷移クリープひずみ則は、(4)の技術で取得した「遷移クリープひずみ速度と定常クリープひずみ速度の比」と、その比を取得した時点での遷移クリープひずみの関係を図11のようにプロットし、その近似曲線から数6中の定数の値を決定することで定式化する。
Technique (5): The material constant of the steady creep rule is determined by the procedure (i) of technique (4).
The transition creep strain law plots the relationship between the “transition creep strain rate and steady creep strain rate” obtained by the technique (4) and the transition creep strain at the time when the ratio is obtained as shown in FIG. The formulation is formulated by determining the value of the constant in Equation 6 from the approximate curve.
Claims (5)
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