{"id":25825,"date":"2024-08-12T10:51:10","date_gmt":"2024-08-12T07:21:10","guid":{"rendered":"https:\/\/caeassistant.com\/?p=25825"},"modified":"2026-06-06T15:34:15","modified_gmt":"2026-06-06T12:04:15","slug":"%e5%a4%8d%e5%90%88%e6%9d%90%e6%96%99%e5%9b%ba%e5%8c%96%e8%bf%87%e7%a8%8b%e8%a7%86%e9%a2%91","status":"publish","type":"post","link":"https:\/\/dev.caeassistant.com\/zh\/%e5%8d%9a%e5%ae%a2\/%e5%a4%8d%e5%90%88%e6%9d%90%e6%96%99%e5%9b%ba%e5%8c%96%e8%bf%87%e7%a8%8b%e8%a7%86%e9%a2%91\/","title":{"rendered":"\u590d\u5408\u6750\u6599\u56fa\u5316\u8fc7\u7a0b\u7684\u57fa\u672c\u539f\u7406"},"content":{"rendered":"

What is Composite curing?<\/strong> Composite curing<\/strong> is a critical thermal and chemical process that transforms a mixture of fibers and a polymer matrix into a rigid fiber-reinforced composite. Through controlled temperature and pressure cycles, curing induces molecular cross-linking, which is essential for achieving the material’s final structural integrity and mechanical performance.<\/span><\/p>\n

Without precise thermal management, these materials fail to meet the rigorous demands of real-world engineering applications. Because optimizing these parameters experimentally is costly, engineers increasingly rely on advanced computational methods to design effective thermal cycles.<\/span><\/p>\n

Here at CAE \u52a9\u624b<\/strong><\/a><\/span>, this comprehensive guide details the core fundamentals of fiber-reinforced composites and examines standard curing methodologies used in modern manufacturing. Furthermore, we demonstrate how to leverage Abaqus simulation software\u2014specifically utilizing custom Fortran subroutines\u2014to accurately model the composite curing process. This provides engineers, researchers, and students with a practical framework to optimize curing cycles, improve composite quality, and reduce production defects. <\/span><\/p>\n

To ensure the model can properly address the needs of a wide range of users\u2014from beginners to advanced industrial applications requiring high accuracy\u2014various material models have been implemented and developed within these subroutines, including linear elastic instantaneously hardening (Chile), path-dependent, and viscoelastic models.<\/span><\/p>\n

\u4ec0\u4e48\u662f\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff08FRC\uff09\uff1f<\/span><\/h2>\n

\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u662f\u4e00\u7c7b\u7531\u4e24\u4e2a\u4e3b\u8981\u76f8\u7ec4\u6210\u7684\u6750\u6599\uff1a\u589e\u5f3a\u7ea4\u7ef4\uff08\u76f81\uff09\u5d4c\u5165\u57fa\u4f53\uff08\u76f82\uff09\u4e2d\u3002\u7136\u800c\uff0c\u4e00\u4e9b\u6587\u732e\u5c06\u57fa\u4f53\u4e0e\u7ea4\u7ef4\u4e4b\u95f4\u7684\u754c\u9762\u89c6\u4e3a\u4e00\u4e2a\u5355\u72ec\u7684\u76f8\u3002\u56fe1\u5c55\u793a\u4e86\u4e00\u5757\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u3002 \u5408\u6210\u7684<\/span>.<\/span><\/p>\n

\"\"<\/p>\n

\u56fe1\uff1a\u4e00\u5757\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599<\/p>\n

\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff08FRC\uff09\u4e2d\u7684\u7ea4\u7ef4\u901a\u5e38\u7531\u9ad8\u521a\u6027\u6750\u6599\u5236\u6210\uff0c\u4ee5\u63d0\u4f9b\u8db3\u591f\u7684\u5f3a\u5ea6\u3002\u57fa\u4f53\uff08\u901a\u5e38\u4e3a\u67d0\u79cd\u805a\u5408\u7269\uff09\u5c06\u7ea4\u7ef4\u7c98\u5408\u5728\u4e00\u8d77\uff0c\u5e76\u5728\u7ea4\u7ef4\u4e4b\u95f4\u4f20\u9012\u5e94\u529b\u3002\u5f53\u8fd9\u4e24\u79cd\u7ec4\u5206\u7ed3\u5408\u5728\u4e00\u8d77\u65f6\uff0c\u5c31\u5f62\u6210\u4e86\u5177\u6709\u72ec\u7279\u6027\u80fd\u7684\u590d\u5408\u6750\u6599\u3002\u8fd9\u79cd\u590d\u5408\u6750\u6599\u8f7b\u8d28\u9ad8\u5f3a\uff0c\u56e0\u6b64\u9002\u7528\u4e8e\u5404\u79cd\u5e94\u7528\u3002.<\/span><\/p>\n

Common types of FRCs<\/span><\/h2>\n

\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599<\/span> \u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff08FRC\uff09\u662f\u4e00\u4e2a\u7edf\u79f0\uff0c\u6db5\u76d6\u4e86\u4e00\u7cfb\u5217\u5177\u6709\u4e0d\u540c\u6027\u80fd\u7684\u6750\u6599\u3002\u6839\u636e\u7ea4\u7ef4\u548c\u57fa\u4f53\u7684\u7279\u6027\uff0cFRC \u53ef\u4ee5\u5206\u4e3a\u591a\u79cd\u7c7b\u578b\u3002\u6bcf\u79cd\u7c7b\u578b\u90fd\u5177\u6709\u5176\u72ec\u7279\u7684\u6027\u80fd\uff0c\u9002\u7528\u4e8e\u7279\u5b9a\u7684\u5e94\u7528\u3002.<\/span><\/p>\n

\u56fe2\u5c55\u793a\u4e86\u57fa\u4e8e\u57fa\u4f53\u6750\u6599\u7684\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff08FRC\uff09\u5206\u7c7b\u3002\u5982\u56fe\u6240\u793a\uff0cFRC\u53ef\u7531\u591a\u79cd\u57fa\u4f53\u6784\u6210\uff0c\u5305\u62ec\u805a\u5408\u7269\u3001\u91d1\u5c5e\u3001\u9676\u74f7\u548c\u78b3\/\u78b3\u6750\u6599\u3002\u5176\u4e2d\uff0c\u805a\u5408\u7269\u57faFRC\u662f\u5e94\u7528\u6700\u5e7f\u6cdb\u7684\u590d\u5408\u6750\u6599\u3002\u805a\u5408\u7269\u57faFRC\u53c8\u53ef\u8fdb\u4e00\u6b65\u5206\u4e3a\u4e24\u7c7b\uff1a\u70ed\u5851\u6027\u590d\u5408\u6750\u6599\u548c\u70ed\u56fa\u6027\u590d\u5408\u6750\u6599\u3002.<\/span><\/p>\n

\"\u57fa\u4e8e\u77e9\u9635\u7684\u590d\u5408\u7c7b\u522b\"<\/p>\n

\u56fe 2\uff1a\u57fa\u4e8e\u57fa\u4f53\u6750\u6599\u7684\u590d\u5408\u6750\u6599\u5206\u7c7b<\/p>\n

\u70ed\u5851\u6027\u5851\u6599\u662f\u4e00\u79cd\u805a\u5408\u7269\u57fa\u4f53\u6750\u6599\uff0c\u56fa\u5316\u540e\u53ef\u4ee5\u91cd\u65b0\u7194\u5316\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u70ed\u56fa\u6027\u5851\u6599\u4e00\u65e6\u52a0\u70ed\u5c31\u4f1a\u6c38\u4e45\u56fa\u5316\u3002\u56fe3\u6bd4\u8f83\u4e86\u70ed\u5851\u6027\u5851\u6599\u548c\u70ed\u56fa\u6027\u5851\u6599\u57fa\u4f53\u5728\u56fa\u5316\u540e\u91cd\u65b0\u52a0\u70ed\u65f6\u7684\u6027\u80fd\u3002.<\/span><\/p>\n

\"\u70ed\u5851\u6027\u548c\u70ed\u56fa\u6027\u57fa\u4f53\u5728\u518d\u52a0\u70ed\u65f6\"<\/p>\n

\u56fe3\uff1a\u70ed\u5851\u6027\u57fa\u4f53\u548c\u70ed\u56fa\u6027\u57fa\u4f53\u5728\u518d\u52a0\u70ed\u8fc7\u7a0b\u4e2d\u7684\u884c\u4e3a\u6bd4\u8f83<\/p>\n

\u70ed\u56fa\u6027\u590d\u5408\u6750\u6599\u662f\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\uff08FRC\uff09\u4e2d\u4e00\u4e2a\u6db5\u76d6\u8303\u56f4\u5e7f\u6cdb\u7684\u7c7b\u522b\uff0c\u5177\u6709\u591a\u79cd\u7c7b\u578b\u548c\u5e94\u7528\u3002\u56fe4\u6839\u636e\u57fa\u4f53\u548c\u7ea4\u7ef4\u6750\u6599\u5bf9\u70ed\u56fa\u6027\u590d\u5408\u6750\u6599\u8fdb\u884c\u4e86\u5206\u7c7b\uff0c\u7a81\u663e\u4e86\u5b83\u4eec\u7684\u591a\u6837\u6027\u3002\u867d\u7136\u672c\u6587\u4e3b\u8981\u5173\u6ce8\u70ed\u56fa\u6027\u590d\u5408\u6750\u6599\uff0c\u4f46\u70ed\u5851\u6027\u590d\u5408\u6750\u6599\u5728FRC\u884c\u4e1a\u4e2d\u4e5f\u53d1\u6325\u7740\u91cd\u8981\u4f5c\u7528\u3002.<\/span><\/p>\n

\"\u70ed\u56fa\u6027\u590d\u5408\u6750\u6599\u5206\u7c7b\"<\/p>\n

\u56fe 4\uff1a\u57fa\u4e8e\u57fa\u4f53\u548c\u7ea4\u7ef4\u6750\u6599\u7684\u70ed\u56fa\u6027\u590d\u5408\u6750\u6599\u5206\u7c7b<\/p>\n\n\n\n
\u6d4f\u89c8\u6211\u4eec\u5185\u5bb9\u5168\u9762\u7684 Abaqus \u6559\u7a0b\u9875\u9762\uff0c\u5176\u4e2d\u5305\u542b\u514d\u8d39\u7684 PDF \u6307\u5357\u548c\u9002\u5408\u6240\u6709\u6280\u80fd\u6c34\u5e73\u7684\u8be6\u7ec6\u89c6\u9891\u3002\u63a2\u7d22\u514d\u8d39\u548c\u4ed8\u8d39\u5957\u9910\uff0c\u4ee5\u53ca\u9ad8\u6548\u638c\u63e1 Abaqus \u7684\u5fc5\u5907\u4fe1\u606f\u3002\u7acb\u5373\u5f00\u542f\u60a8\u7684 Abaqus \u5b66\u4e60\u4e4b\u65c5\uff01 Abaqus\u6559\u7a0b<\/a><\/span> \u73b0\u5728\uff01<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

What is the composite curing process?<\/span><\/h2>\n

\u56fa\u5316\u662f\u6307\u5bf9\u590d\u5408\u6750\u6599\u65bd\u52a0\u70ed\u91cf\u548c\u538b\u529b\uff0c\u4f7f\u5176\u57fa\u4f53\u5931\u53bb\u6d41\u52a8\u6027\u7684\u8fc7\u7a0b\u3002\u590d\u5408\u6750\u6599\u7684\u56fa\u5316\u8fc7\u7a0b\u5fc5\u987b\u4e25\u683c\u63a7\u5236\uff0c\u624d\u80fd\u4f7f\u6700\u7ec8\u590d\u5408\u6750\u6599\u8fbe\u5230\u6240\u9700\u7684\u6027\u80fd\u548c\u8d28\u91cf\u3002.<\/span><\/p>\n

Today, three well-established methods are commonly used for the composite curing process: autoclave, oven curing, and heated die curing (pultrusion). In general, oven-curing is a traditional method, that utilizes a standard oven to apply heat to the composite. As depicted in Figure 5, it needs a vacuum bag to apply pressure and remove the air. Despite its lower cost compared to the autoclave method, oven curing results in higher porosity and lower mechanical properties.<\/span><\/p>\n

\"\u70d8\u7bb1\u56fa\u5316\u8fc7\u7a0b\"<\/p>\n

Figure 5: Schematic representation of the oven-curing process [\u53c2\u8003\u8d44\u6599.<\/a>]<\/p>\n

The autoclave method is more advanced than the oven-curing. It utilizes a pressure vessel (autoclave) to apply both heat and pressure simultaneously to the composite, as shown in Figure 6. This process enables the production of high-quality laminates with low porosity and superior mechanical properties. However, unlike oven curing, the autoclave method is more expensive and requires complex equipment.<\/span><\/p>\n

\"\u9ad8\u538b\u706d\u83cc\u88c5\u7f6e\"<\/p>\n

Figure 6: An autoclave device [\u53c2\u8003\u8d44\u6599.<\/a>]<\/p>\n

Heated die curing, particularly in the context of pultrusion, offers several advantages over traditional oven and autoclave curing methods, especially for continuous composite manufacturing. For example, unlike oven and autoclave curing, which are batch processes, pultrusion with a heated die (figure 7) enables continuous production. Moreover, since heat is applied directly to the material through the die, heat loss is minimized, leading to reduced curing time. Additionally, the die not only heats but also shapes the part during curing, resulting in excellent dimensional accuracy and surface finish without the need for secondary machining. Therefore, this method can be considered a cost-effective and high-quality approach to composite curing.<\/span><\/p>\n

\"\u62c9\u6324\u6210\u578b\u673a\"<\/p>\n

Figure 7: A pultrusion machine<\/p>\n

How the composite curing process affects the product quality?<\/h3>\n

During the composite curing process, FRCs experience specific pressure and temperature cycles to achieve optimal quality. However, the standard composite curing process can last several hours, making it inefficient for industrial production. Manufacturers prefer to shorten the curing cycles by applying higher temperatures within shorter time periods. While this approach can increase production speed, it may impact the product quality and lead to residual deformations. Figure 8 showcases a product that experienced residual deformations after the composite curing process.<\/span><\/p>\n

\"\u590d\u5408\u6750\u6599\u4e2d\u7684\u6b8b\u4f59\u53d8\u5f62\"<\/p>\n

Figure 8: Schematic representation of the residual deformations in a composite [\u53c2\u8003\u8d44\u6599.<\/a>]<\/p>\n

\u4f20\u7edf\u4e0a\uff0c\u5e73\u8861\u751f\u4ea7\u6548\u7387\u548c\u8d28\u91cf\u7684\u65b9\u6cd5\u662f\u9488\u5bf9\u6bcf\u79cd\u4ea7\u54c1\u8fdb\u884c\u591a\u6b21\u56fa\u5316\u5b9e\u9a8c\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u65b9\u6cd5\u65e2\u8017\u65f6\u53c8\u8d39\u529b\u3002\u8fd9\u5c31\u51f8\u663e\u4e86\u8bbe\u8ba1\u6700\u4f73\u56fa\u5316\u5de5\u827a\u4ee5\u786e\u4fdd\u4ea7\u54c1\u8d28\u91cf\u548c\u751f\u4ea7\u6548\u7387\u7684\u6311\u6218\u3002\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u662f\u5e94\u5bf9\u8fd9\u4e00\u6311\u6218\u7684\u4e00\u79cd\u65b9\u6cd5\u3002.<\/span><\/p>\n

Fiber reinforced composite curing simulation<\/span><\/h2>\n

\u6570\u503c\u65b9\u6cd5\u7b80\u5316\u4e86 \u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df<\/strong>. \u5b83\u4eec\u662f\u8bbe\u8ba1\u56fa\u5316\u5de5\u827a\u6d41\u7a0b\u65f6\uff0c\u66ff\u4ee3\u5b9e\u9a8c\u6d4b\u8bd5\u7684\u6709\u6548\u65b9\u6cd5\u3002\u8fd9\u4e9b\u65b9\u6cd5\u7b80\u5316\u4e86\u4f18\u5316\u56fa\u5316\u5de5\u827a\u6d41\u7a0b\u7684\u8bbe\u8ba1\uff0c\u65e2\u80fd\u786e\u4fdd\u6240\u9700\u7684\u4ea7\u54c1\u8d28\u91cf\uff0c\u53c8\u80fd\u7ef4\u6301\u9ad8\u6548\u7684\u751f\u4ea7\u3002\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u5fc5\u987b\u540c\u65f6\u8003\u8651\u5316\u5b66\u3001\u70ed\u548c\u529b\u5b66\u4e09\u4e2a\u8026\u5408\u573a\uff0c\u56e0\u6b64\u88ab\u79f0\u4e3a\u70ed-\u5316\u5b66-\u529b\u5b66\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u3002.<\/span><\/p>\n

Simulation of the thermo-chemical reactions in the curing process<\/h3>\n

\u5728 \u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df<\/strong>, \u70ed\u91cf\u6765\u6e90\u4e8e\u4e24\u4e2a\u65b9\u9762\uff1a\u5916\u90e8\u548c\u5185\u90e8\u3002\u8ba1\u7b97 \u5916\u90e8\u52a0\u70ed<\/em> \u5728\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u4e2d\uff0c\u8ba1\u7b97\u76f8\u5bf9\u7b80\u5355\u3002\u7136\u800c\uff0c\u8ba1\u7b97\u2026\u2026 \u5185\u90e8\u70ed\u91cf<\/em> within the composite curing simulation is a challenging task. Internal heat arises from the chemical reactions within the composite during curing. Therefore, we need a thermo-chemical model to account for the internal heat within the composite curing simulation. In such a model, the generated heat is a function of the degree of cure. Note that the degree of cure is a parameter between zero and one, that represents the extent of curing. A value of zero indicates an uncured composite, while a value of one represents a fully cured one. Figure 9 compares the applied temperature and the temperature developed during curing within a composite. The difference represents the internal heat generation, predicted by the composite curing simulation.<\/span><\/p>\n

\"\u56fa\u5316\u8fc7\u7a0b\u4e2d\u7684\u6e29\u5ea6\u6bd4\u8f83\"<\/p>\n

Figure 9: Comparison of the applied temperature and the temperature developed in a composite during curing<\/p>\n

\u4e3a\u4e86\u66f4\u6df1\u5165\u5730\u4e86\u89e3\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\uff0c\u60a8\u53ef\u4ee5\u63a2\u7d22\u6211\u4eec\u7684\u5b66\u4e60\u8d44\u6599\u5305\u201c\u5728Abaqus\u4e2d\u8fdb\u884c\u56fa\u5316\u8fc7\u7a0b\u6a21\u62df<\/span><\/strong><\/a>\u201c\u5b83\u63d0\u51fa\u4e86\u8ba1\u7b97\u56fa\u5316\u8fc7\u7a0b\u4e2d\u5185\u90e8\u70ed\u91cf\u7684\u516c\u5f0f\uff0c\u7279\u522b\u5173\u6ce8\u4f17\u6240\u5468\u77e5\u7684 AS4\/3501-6 \u9884\u6d78\u6599\u3002.<\/span><\/p>\n

Evaluation of stress components during the composite curing simulation<\/h3>\n

Stress prediction is a challenge for the numerical simulation of the composite curing process. This challenge arises due to the changes in the resin’s modulus of elasticity. It makes the composite curing simulation complex. As illustrated in Figure 10, the modulus starts very low and rises significantly during curing as chemical reactions take place. Finally, it reaches a constant value.<\/span><\/p>\n

\"\u56fa\u5316\u8fc7\u7a0b\u4e2d\u6811\u8102\u6a21\u91cf\u7684\u53d8\u5316\"<\/p>\n

Figure 10: Schematic representation of the resin modulus variation during the curing process [\u53c2\u8003\u6587\u732e]<\/a><\/p>\n

\u4e3a\u4e86\u6355\u6349\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u8fc7\u7a0b\u4e2d\u6811\u8102\u6a21\u91cf\u7684\u53d8\u5316\uff0c\u4eba\u4eec\u63d0\u51fa\u4e86\u591a\u79cd\u6a21\u578b\u3002\u8fd9\u4e9b\u6a21\u578b\u5305\u62ec\u7ebf\u5f39\u6027\u6a21\u578b\u3001\u7c98\u5f39\u6027\u6a21\u578b\u548c\u8def\u5f84\u76f8\u5173\u6a21\u578b\u3002\u6bcf\u79cd\u6a21\u578b\u90fd\u6709\u5176\u81ea\u8eab\u7684\u4f18\u52bf\u548c\u5c40\u9650\u6027\u3002\u88681\u603b\u7ed3\u4e86\u4e13\u95e8\u7528\u4e8e\u8ba1\u7b97AS4\/3501-6\u9884\u6d78\u6599\u4e2d\u6811\u8102\u6a21\u91cf\u6216\u5e94\u529b\u5206\u91cf\u7684\u6a21\u578b\u3002\u60a8\u53ef\u4ee5\u67e5\u770b\u8fd9\u7bc7\u6587\u7ae0\u201c\u5229\u7528\u591a\u7269\u7406\u573a\u8026\u5408\u5206\u6790\u548c\u591a\u79cd\u672c\u6784\u6a21\u578b\u7814\u7a76\u56fa\u5316\u5faa\u73af\u5bf9\u539a\u590d\u5408\u6750\u6599\u6b8b\u4f59\u5e94\u529b\u7684\u5f71\u54cd<\/span><\/span><\/a>\u201d\u6709\u5173\u8fd9\u4e9b\u6a21\u578b\u7684\u66f4\u591a\u8be6\u7ec6\u4fe1\u606f\uff0c\u8bf7\u53c2\u9605\u76f8\u5173\u6587\u6863\u3002\u5b83\u4eec\u7b80\u5316\u4e86\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u3002.<\/span><\/p>\n\n\n\n\n\n\n\n\n
\u7c7b\u522b<\/th>\n\u6a21\u578b<\/th>\n\u6570\u5b66\u516c\u5f0f<\/th>\n<\/tr>\n<\/thead>\n
Linear-elastic<\/td>\nChile ($\\alpha$)<\/td>\n$E_m = (1-\\alpha)E_m^0 + \\alpha E_m^{\\infty}$<\/td>\n<\/tr>\n
Chile ($T$)<\/td>\n$E_m = \\begin{cases} E_m^0 & T_* \\le T_{c1} \\\\ \\left( \\frac{T_{c2}-T_*}{T_{c2}-T_{c1}} \\right) E_m^0 + \\left( \\frac{T_*-T_{c1}}{T_{c2}-T_{c1}} \\right) E_m^{\\infty} & T_{c1} < T_* < T_{c2} \\\\ E_m^{\\infty} & T_* \\ge T_{c2} \\end{cases}$<\/td>\n<\/tr>\n
\u7c98\u5f39\u6027<\/td>\nGeneral Model<\/td>\n$\\sigma_i(t) = \\int_{0}^{t} C_{ij}(\\xi-\\xi’) \\frac{\\partial \\epsilon_j}{\\partial \\xi’} d\\xi’$<\/td>\n<\/tr>\n
Path-dependent<\/td>\nTemperature Dependent<\/td>\n$\\sigma_i = \\begin{cases} C_{ij}^0 \\epsilon_j & T \\ge T_g \\\\ C_{ij}^1 \\epsilon_j – (C_{ij}^1 – C_{ij}^0) \\epsilon_j |_{t=t_{vit}} & T < T_g \\end{cases}$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u88681\u4e2d\uff0c \u524d\u4e24\u4e2a\u65b9\u7a0b\uff08\u7ebf\u6027\u5f39\u6027\uff09\u6a21\u578b<\/strong> \u7528\u4e8e\u6a21\u62df\u56fa\u5316\u8fc7\u7a0b\uff0c\u60a8\u53ef\u4ee5 \u5b66\u4e60\u8fd9\u4e9b\u65b9\u7a0b\u5f0f<\/strong> \u548c \u5982\u4f55\u5bf9\u5b83\u4eec\u8fdb\u884c\u5efa\u6a21<\/strong> \u5b8c\u5168\u5728 Curing process simulation in Abaqus Tutorial<\/strong><\/a><\/span>.<\/span><\/span><\/p>\n

Also, the next two equations (\u7c98\u5f39\u6027\u548c\u8def\u5f84\u4f9d\u8d56\u6027<\/strong><\/span><\/a>\u6a21\u578b\u7528\u4e8e \u6cbb\u6108\u6a21\u62df<\/strong> \u5728\u4e0b\u9762\u7684\u5305\u88f9\u4e2d\u3002.<\/span><\/span><\/p>\n\n

\u6211\u4eec\u8be6\u7ec6\u63cf\u8ff0\u4e86\u7ebf\u6027\u5f39\u6027\u6a21\u578b\uff0c\u5e76\u63d0\u4f9b\u4e86\u5728\u6240\u63d0\u4f9b\u8f6f\u4ef6\u5305\u4e2d\u5b9e\u73b0\u8fd9\u4e9b\u6a21\u578b\u7684\u5206\u6b65\u6307\u5357\u3002\u8fd9\u7b80\u5316\u4e86\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u3002\u4e3a\u4e86\u9a8c\u8bc1\u6a21\u578b\u7684\u6709\u6548\u6027\uff0c\u6211\u4eec\u5c06\u7ed3\u679c\u4e0e\u53c2\u8003\u89e3\u8fdb\u884c\u4e86\u6bd4\u8f83\uff0c\u5982\u56fe 21 \u6240\u793a\u3002.<\/span><\/p>\n

\"\u4e0e\u53c2\u8003\u6eb6\u6db2\u7684\u5e94\u529b\u6bd4\u8f83\"<\/p>\n

Figure 11: Comparison of the stress in a composite with the reference solution<\/p>\n

\u603b\u4e4b\uff0c\u6570\u503c\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u9700\u8981\u540c\u65f6\u8003\u8651\u70ed\u573a\u3001\u5316\u5b66\u573a\u548c\u529b\u5b66\u573a\u3002\u60a8\u53ef\u80fd\u60f3\u77e5\u9053\u5982\u4f55\u5b9e\u73b0\u5982\u6b64\u590d\u6742\u7684\u6a21\u578b\uff0c\u4f46\u522b\u62c5\u5fc3\uff01\u6211\u4eec\u5c06\u6307\u5bfc\u60a8\u91c7\u7528\u4e00\u79cd\u51c6\u786e\u9ad8\u6548\u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e00\u96be\u9898\u3002.<\/span><\/p>\n

\u7ea4\u7ef4\u589e\u5f3a\u6df7\u51dd\u571f\u517b\u62a4\u8fc7\u7a0b\u4e2d\u7684\u5e94\u53d8\u8bc4\u4f30<\/h3>\n

\u590d\u5408\u6750\u6599\u7684\u56fa\u5316\u8fc7\u7a0b\u4f1a\u5bfc\u81f4\u4e0d\u826f\u53d8\u5f62\uff0c\u4ece\u800c\u5bf9\u4ea7\u54c1\u8d28\u91cf\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\u3002\u4e3a\u4e86\u6700\u5927\u9650\u5ea6\u5730\u51cf\u5c11\u8fd9\u4e9b\u53d8\u5f62\uff0c\u6211\u4eec\u5e94\u8be5\u5728\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u4e2d\u8003\u8651\u6b8b\u4f59\u5e94\u53d8\u3002.<\/span><\/p>\n

\u5728\u56fa\u5316\u8fc7\u7a0b\u4e2d\uff0c\u590d\u5408\u6750\u6599\u4f1a\u7ecf\u5386\u4e24\u79cd\u7c7b\u578b\u7684\u5e94\u53d8\uff1a\u673a\u68b0\u5e94\u53d8\u548c\u975e\u673a\u68b0\u5e94\u53d8\u3002\u590d\u5408\u6750\u6599\u4e2d\u7684\u975e\u673a\u68b0\u5e94\u53d8\u6765\u6e90\u4e8e\u56fa\u5316\u6536\u7f29\u548c\u70ed\u81a8\u80c0\u3002\u56fa\u5316\u6536\u7f29\u662f\u7531\u4e8e\u56fa\u5316\u8fc7\u7a0b\u4e2d\u57fa\u4f53\u4e2d\u6c14\u4f53\u548c\u6eb6\u5242\u7684\u91ca\u653e\u9020\u6210\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u56fa\u5316\u6536\u7f29\u3002.<\/span><\/p>\n

$$\\varepsilon_{cu} = \\mathbf{CCS} \\, \\Delta \\alpha$$<\/p>\n

\u5728\u8fd9\u4e2a\u7b49\u5f0f\u4e2d\uff0c, CCS<\/strong><\/em> represents the effective chemical shrinkage coefficient of the matrix, and \u2206\u03b1 is the variation in the degree of cure. Figure 12 schematically illustrates how the chemical shrinkage occurs during the curing process.<\/span><\/p>\n

\"\u56fa\u5316\u8fc7\u7a0b\u4e2d\u7684\u5316\u5b66\u6536\u7f29\u6548\u5e94\"<\/p>\n

Figure 12: Illustration of the chemical shrinkage effect during the curing process (Adapted form [\u53c2\u8003\u8d44\u6599.<\/a>\uff08\u7ecf\u8fc7\u4fee\u6539\uff09<\/p>\n

\u70ed\u81a8\u80c0\u7cfb\u6570\u53d6\u51b3\u4e8e\u5916\u90e8\u65bd\u52a0\u7684\u70ed\u91cf\u548c\u56fa\u5316\u8fc7\u7a0b\u4e2d\u4ea7\u751f\u7684\u5185\u90e8\u70ed\u91cf\u3002\u7531\u4e8e\u5185\u90e8\u70ed\u91cf\u53d6\u51b3\u4e8e\u56fa\u5316\u7a0b\u5ea6\uff0c\u56e0\u6b64\u70ed\u81a8\u80c0\u7cfb\u6570\u4e5f\u53d7\u5316\u5b66\u53cd\u5e94\u7684\u5f71\u54cd\u3002\u60a8\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8fdb\u884c\u8ba1\u7b97\u3002.<\/span><\/p>\n

$$\\varepsilon_{th} = \\boldsymbol{CTE} \\, \\Delta T$$<\/p>\n

\u5728\u54ea\u91cc CTE<\/strong><\/em>\u00a0\u662f\u590d\u5408\u6750\u6599\u7684\u70ed\u81a8\u80c0\u7cfb\u6570\uff0c\u662f\u5176\u6e29\u5ea6\u53d8\u5316\u3002.<\/span><\/p>\n

In summary, several factors influence the total strain experienced by composites during curing, as detailed in Figure 13.<\/span><\/p>\n

\"\u590d\u5408\u6750\u6599\u5728\u56fa\u5316\u8fc7\u7a0b\u4e2d\u4ea7\u751f\u7684\u5e94\u53d8\u5206\u91cf\"<\/p>\n

Figure 13: An overview of the strain components generated in a composite during the curing process<\/p>\n

\u5728\u7ea4\u7ef4\u589e\u5f3a\u590d\u5408\u6750\u6599\u56fa\u5316\u6a21\u62df\u4e2d\u540c\u65f6\u8003\u8651\u6240\u6709\u5e94\u53d8\u5206\u91cf\u53ef\u80fd\u5177\u6709\u6311\u6218\u6027\u3002\u7136\u800c\uff0c\u201c\u5728Abaqus\u4e2d\u8fdb\u884c\u56fa\u5316\u8fc7\u7a0b\u6a21\u62df<\/span><\/strong><\/a>” learning package on our website simplifies this process. It offers a step-by-step guide on calculating strain components during composite curing simulation. For validation, we compared our results with a reference solution, as shown in Figure 14.<\/span><\/p>\n

\"\u603b\u5e94\u53d8\u4e0e\u53c2\u8003\u503c\u7684\u6bd4\u8f83\"<\/p>\n

Figure 14: Comparison of the total strain in the composite with the reference solution<\/p>\n

Abaqus\u56fa\u5316\u8fc7\u7a0b\u6a21\u62df<\/span><\/h2>\n

Abaqus is a widely used finite element program, that has simplified the fiber reinforced composite curing simulation.<\/span><\/p>\n

\"\"<\/span><\/p>\n

It has been extensively used in published papers to analyze internal heat generation and mechanical fields during the composite curing process. However, the lack of required thermo-chemo-mechanical models in Abaqus presents a significant challenge for Abaqus curing process simulation.<\/span><\/p>\n

\"\"<\/span><\/p>\n

Fortunately, Abaqus user-defined subroutines provide a powerful solution to overcome this challenge.<\/span><\/p>\n