ＴＨＥＲＥＬＡＴＩＯＮＳＨＩＰＳＢＥＴＷＥＥＮＧＬＯＢＡＬＡＮＤＥＶＥＲＹＬＡＹＥＲＤＥ ＦＯＲＭＡＴＩＯＮＴＥＸＴＵＲＥＳＯＦ７０－３０ＢＲＡＳＳＲＯＬＬＥＤＢＹＣＲＯＳＳＳ ＨＥＡＲＲＯＬＬＩＮＧ￥Ｚｈａｏ，Ｘｉａｎｇ；Ｚｕｏ，Ｌｉａｎｇ；Ｚｈａｏ，Ｈｏｎｇ； Ｌｉａｎｇ，Ｚｈｉｄｅ（ＤｅｐｔａｒｔｍｅｎｔｏｆＭａｔｅｒｉａｌＳｃｉｅｎｃｅａｎｄ Ｅｎｇｉｎｅｅｒｉｎｇ，ＮｏｒｔｈｅａｓｔｅｒｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈｅｎｙａｎｇ １１０００６）Ａｂｓｔｒａｃｔ：Ｇｌｏｂａｌａｎｄｅｖｅｒｙｌａｙｅｒｄｅｆｏｒｍａｔ ｉｏｎｔｅｘｔｕｒｅｓｗｅｒｅｄｅｓｃｒｉｂｅｄａｎｄｔｈｅｒｅｌａｔｉｏｎｓｈｉｐｂ ｅｔｗｅｅｎｔｈｅｍｗｅｒｅｉｎｖｅｓｔｉｇａｔｅｄｂｙｔｈｒｅｅｄｉｍｅｎｓｉｏｎａ ｌｏｒｉｅｎｔａｔｉｏｎｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎ．Ｉｔｗａｓｆｏｕｎｄ ｔｈａｔｔｈｅｍａｃｒｏｓｃｏｐｉｃｓｔａｔｉｓｔｉｃａｌｕｎｓｙｍｍｅｔｒｙｏｆｇｌ ｏｂａｌｔｅｘｔｕｒｅｉｓｎｏｔｔｈｅｓａｍｅａｓｔｈａｔｏｆｅｖｅｒｙｌａｙｅｒｔｅ ｘｔｕｒｅ，ｂｕｔｃｏｎｓｉｓｔｅｎｔｗｉｔｈｔｈａｔｏｆｂｅｓｉｄｅｓｌｏｗｓｐｅｅ ｄｒｏｌｌｅｒ，ｔｈｅｒｅｓｕｌｔｓｗｈｉｃｈｗｅｒｅａｄｄｅｄａｎｄａｖｅｒａｇｅｄ ｂｙ５ｌａｙｅｒｓＯＤＦｄｏｎｏｔｒｅｐｒｅｓｅｎｔｇｌｏｂａｌｔｅｘｔｕｒｅ．Ｋｅｙ ｗｏｒｄｓ：ｃｒｏｓｓｓｈｅａｒｒｏｌｌｉｎｇｍａｃｒｏｓｃｏｐｉｃｓｔａｔｉｓｔｉｃ ａｌｕｎｓｙｍｍｅｔｒｙｔｅｘｔｕｒｅｔｈｒｅｅｄｉｍｅｎｓｉｏｎａｌｏｒｉｅｎｔａｔ ｉｏｎｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎ（ＯＤＦ）１ＩＮＴＲＯＤＵＣＴＩＯＮＴｈ ｅｕｎｓｙｍｍｅｔｒｉｃｐｌａｓｔｉｃｆｌｏｗｐｒｏｄｕｃｅｄｂｙｃｒｏｓｓｓｈｅａｒ ｒｏｌｌｉｎｇｉｎｓｉｎｇｌｅｄｉｒｅｃｔｏｎｒｅｓｕｌｔｓｉｎｍａｃｒｏｓｃｏｐｉｃ ｓｔａｔｉｓｔｉｃａｌｕｎｓｙｍｍｅｔｒｉｅｓｏｆｔｅｘｔｕｒｅｉｎｇｌｏｂａｌａｎｄ ｅｖｅｒｙｌａｙｅｒ［１－２］，ｔｈｉｓｋｉｎｄｏｆｕｎｓｙｍｍｅｔｒｙｃａｎｌｅａｄ ｄｉｒｅｃｔｌｙｔｈｅｃｈａｎｇｅｏｆｒｏｌｌｅｄｐｌａｔｅｐｒｏｐｅｒｔｙ，ｔｈｅｒ ｅｆｏｒｅ，ｉｔｉｓｉｍｐｏｒｔａｎｔｔｏｒｅｓｅａｒｃｈｔｈｅｍａｃｒｏｓｃｏｐｉｃ ｓｔａｔｉｓｔｉａｌｕｎｓｖｍｍｅｔｒｉｅｓｏｆｔｅｘｔｕｒｅ．Ｉｎｔｈｉｓｐａｐｅｒ ，ｔｈｅｕｎｓｙｍｍｅｔｒｉｅｓｏｆｔｅｘｔｕｒｅｉｎｇｌｏｂａｌａｎｄｅｖｅｒｙｌａ ｙｅｒｏｆ７０－３０ｂｒａｓｓｒｏｌｌｅｄｂｙｃｒｏｓｓｓｈｅａｒｒｏｌｌｉｎｇｉｎｓ ｉｎｇｌｅｄｉｒｅｃｔｉｏｎａｒｅｄｉｓｃｒｉｂｅｄａｎｄｔｈｅｒｅｌａｔｉｏｎｂｅｔ ｗｅｎｇｌｏｂａｌａｎｄｅｖｅｒｙｌａｙｅｒｔｅｘｔｕｒｅｓｉｓｉｎｖｅｓｔｉｇａｔｅ ｄｂｙｔｈｅｔｈｒｅｅｄｉｍｅｎｔｉｏｎａｌｏｒｉｅｎｔａｔｉｏｎｄｉｓｔｒｉｂｕｔｉ ｏｎｆｕｎｃｔｉｏｎ（ＯＤＦ）．２ＥＸＰＥＲＩＭＥＮＴＡＬＣｏｍｍｅｒｃｉａｌ７０－３ ０ｂｒａｓｓ２ｍｍｉｎｔｈｉｃｋｎｅｓｓｗａｓｒｏｌｌｅｄｂｙｃｒｏｓｓｓｈｅａｒｒｏ ｌｌｉｎｇｉｎｓｉｎｇｌｅｄｉｒｅｃｔｉｏｎａｔ９０％ｒｅｄｕｃｔｉｏｎｉｎｔｈｉｃｋ ｎｅｓｓ，ｌｉｎｅａｒｖｅｌｏｃｉｔｉｅｓｒａｔｉｏｏｆｆａｓｔａｎｄｓｌｏｗｓｐｅｅ ｄｒｏｌｌｅｒｓｗａｓ１．２８．Ｔｈｅｎｔｈｅｒｏｌｌｅｄｐｌａｔｅｗａｓｄｉｖｉｄｅ ｄｉｎｔｏｆｉｖｅｌａｙｅｒｓａｌｏｎｇｒｏｌｌｉｎｇｐｌａｎｅｎｏｒｍａｌ，ｆｒｏｍ ｓｕｒｆａｃｅｂｅｓｉｄｅｓｌｏｗｒｏｌｌｅｒ，ｅａｃｈｌａｙｅｒｗａｓｍａｒｋｅｄｂ ｙ０，１／４，１／２，３／４，１ｌａｙｅｒｒｅｓｐｅｃｔｉｖｅｌｙ．Ｓｅｖｅｒａｌｐｉ ｅｃｅｓｏｆｔｅｓｔｅｄｓｈｅｅｔｓｗｅｒｅｇｌｕｅｄｔｏｇｅｔｈｅｒｉｎａｃｃｏｒｄ ａｎｃｅｗｉｔｈｓａｍｅｒｏｌｌｉｎｇｄｉｒｅｃｔｉｏｎｔｏｆｏｒｍａｒｅｃｔａｎｇｌ ｅｂｏｄｙｉｎｗｈｉｃｈａｓｅｃｔｉｏｎｗａｓｃｕｔａｎｄａｎａｒｒｏｗｗａｓｓｉｇｎ ｅｄｉｎｔｈｅｓｅｃｔｉｏｎａｓｉｎｍｅａｓｕｒｅｄｃｏｍｐｏｓｉｔｅｓａｍｐｌｅ｛１ １１｝，｛２００｝ａｎｄ｛２２０｝ｔｈｒｅｅｉｍｃｏｍｐｌｅｔｅｐｏｌｅｆｉｇｕｒｅｓ ａｒｅｍｅａｓｕｒｅｄｂｙｔｈｅＳｃｈｕｌｚｍｅｔｈｏｄ［３］，２０°≤α≤９０°，△ α＝△β＝５°．ＴｈｅｕｎｓｙｍｍｅｔｒｉｃＯＤＦｓｗｅｒｅｃａｌｃｕｌａｔｅｄａｓＬ ｍａｘ＝１６［１４］．ＵｎｄｅｒｔｈｅｃｏｏｒｄｉｎａｔｅＯＡ′Ｂ′Ｃ′ｏｆｔｈｅｃｏ ｍｐｏｓｉｔｅｓａｍｐｌｅ，ｔｈｅｃｏｅｆｆｉｃｉｅｎｔｏｆＯＤＦｉｓＷｌｐｍｗｈｉｃ ｈｃａｎｂｅｔｒａｎｓｆｏｒｍｅｄｉｎｔｏｔｈｅｃｏｏｒｄｉｎａｔｅＯＡＢＣｉｎｗｈｉ ｃｈＲＤ，ＴＤａｎｄＮＤａｒｅｃｈａｒａｃｔｅｒｉｓｔｉｃｄｉｒｅｃｔｉｏｎａｃｃｏｒ ｄｉｎｇｔｏｆｏｒｍｕｌａ［５］ｗｈｅｒｅα，βａｎｄγｉｓＥｕｌｅｒａｎｇｌｅ．ＯＤ ＦｃａｎｂｅｃａｌｃｕｌａｔｅｄｂｙｍｅａｎｓｏｆＷｌｍｍ．①ＲｅｃｅｉｖｅｄＳｅｐｔ ．５，１９９４３ＲＥＳＵＬＴＳＴｈｅＯＤＦｓｅｃｔｉｏｎｓｏｆｃｏｓｔａｎｔψ＝３５° ａｎｄψ＝１４５°ｉｎｅｖｅｒｙｌａｙｅｒａｎｄｇｌｏｂａｌｏｆ７０－３０ｂｒａｓｓｒ ｏｌｌｅｄｂｙｃｒｏｓｓｓｈｅａｒｒｏｌｌｉｎｇｉｎｓｉｎｇｌｅｄｉｒｅｃｔｉｏｎａｒ ｅｓｈｏｗｎｉｎＦｉｇ．１．Ｉｔｉｓｆｏｕｎｄｔｈａｔｍａｉｎｔｅｘｔｕｒｅｓｉｎｅｖ ｅｒｙｌａｙｅｒａｎｄｇｌｏｂａｌａｒｅ｛１１０｝＜１１２＞ｗｈｉｃｈａｒｅｔｈｅｓａ ｍｅａｓｍａｉｎｔｅｘｔｕｒｅｏｆ７０－３０ｂｒａｓｓｒｏｌｌｅｄｂｙｃｏｍｍｏｎｒｏ ｌｌｉｎｇ，Ｆｉｇ．１ψ＝３５°ａｎｄψ＝１４５°ＯＤＦｃｏｓｔａｎｔｓｅｃｔｉｏｎｓ ｏｆｅｖｅｒｙｌａｙｅｒａｎｄｇｌｏｂａｌｔｅｘｔｕｒｅｓ（ａ）─０１ａｙｅｒ；（ｂ） ─１／４ｌａｙｅｒ；（ｃ）─１／２ｌａｙｅｒ；（ｄ）─３／４ｌａｙｅｒ；（ｅ）─１ｌａ ｙｅｒｉ（ｆ）─ａｖｅｒａｇｅｏｆ５ｌａｙｅｒｓｌ；（ｇ）─ｇｌｏｂａｌｂｕｔｔｈｅｉ ｎｔｅｎｓｉｔｙａｎｄｓｃａｔｔｅｒｉｎｇｏｆｅｖｅｒｙｔｅｘｔｕｒｅｃｏｍｐｏｎｅｎ ｔｉｎ｛１１０｝＜１１２＞ａｒｅｄｉｆｆｅｒｅｎｔ，ｔｈａｔｉｓ，ｔｈｅｒｅｉｓａｍａ ｃｒｏｓｃｏｐｉｃｓｔａｔｉｓｔｉｃａｌｕｎｓｙｍｍｅｔｒｙ．Ｉｎ０，１／４ａｎｄ１／ ２ｌａｙｅｒｓ，ｉｎｔｅｎｓｉｔｙｏｆｉｓｗｅａｋｅｒｔｈａｎｔｈａｔｏｆｉｎ３／４ａ ｎｄ１ｌａｙｅｒｓ，ｉｎｔｅｎｓｉｔｙｏｆｉｓｓｔｒｏｎｇｅｒｔｈａｎｔｈａｔｏｆ［１ １２］，ｉｔｉｓｊｕｓｔｃｏｎｔｒａｒｙｗｉｔｈｔｈｅｃｏｎｄｉｔｉｏｎｉｎ１，１／４ ａｎｄ１／２ｌａｙｅｒｓ．Ｓｉｍｕｌａｔｎｅｏｕｓｌｙ，ｔｈｅｕｎｓｙｍｍｅｔｒｙｏｆ ｔｅｘｔｕｒｅｂｅｓｉｄｅｆａｓｔｒｏｌｌｅｒｉｓｓｔｒｏｎｇｅｒｔｈａｎｔｈａｔｂｅ ｓｉｄｅｓｌｏｗｒｏｌｌｅｒ．Ｔｈｅｒｅｓｕｌｔａｄｄｅｄａｎｄａｖｅｒａｇｅｄｆｒｏ ｍＯＤＦｓｏｆｆｉｖｅｌａｙｅｒｓｓｈｏｗｓｔｈａｔｉｎｔｅｎｓｉｔｙｏｆｉｓｓｔｒｏ ｎｇｅｒｔｈａｎｔｈａｔｏｆａｎｄｔｈｅｒｅｓｔｉｌｌｉｓｗｅａｋｅｒｍａｃｒｏｓｃｏ ｐｉｃｓｔａｔｉｓｔｉｃａｌｕｎｓｙｍｍｅｔｒｙ．ＯＤＦｓｅｃｔｉｏｎ（Ｆｉｇ．１（ｇ ））ｃａｌｃｕｌａｔｅｃｆｒｏｍｃｏｍｐｏｓｉｔｅｓａｍｐｌｅｒｅｖｅａｌｓａｍａｃｒ ｏｓｃｏｐｉｃｓｔａｔｉｓｔｉｃａｌｕｎｓｙｍｍｅｔｒｙｏｆｇｌｏｂａｌｔｅｘｔｕｒｅ ，ｔｈａｔｉｓｉｎｔｅｎｓｉｔｙｏｆｉｓｗｅａｋｅｒｔｈａｎｔｈａｔｏｆａｎｄｔｈｅｕ ｎｓｙｍｍｅｔｒｙｉｓｓｔｒｏｎｇｅｒｂｕｔｉｎｔｅｎｓｉｔｙｏｆｔｅｘｔｕｒｅｉｓｗ ｅａｋｅｒ．４ＤＩＳＣＵＳＳＩＯＮＩｎｔｈｅｃｒｏｓｓｓｈｅａｒｒｏｌｌｉｎｇ，ｔｈｅ ｕｎｓｙｍｍｅｔｒｙｏｆｌｉｎｅａｒｖｅｌｏｃｉｔｉｅｓｂｅｔｗｅｅｎｔｈｅｆａｓｔａ ｎｄｓｌｏｗｓｐｅｅｄｒｏｌｌｅｒｓｆｏｒｍｓｔｈｅｃｒｏｓｓｓｈｅａｒｒｏｌｌｉｎｇ ｚｏｎｅ（Ｆｉｇ．２）ｉｎｗｈｉｃｈｓｈｅａｒｆｏｒｃｅｓｔｏｔｈｅｅｘｉｔａｎｄｔｈ ｅｅｎｔｒａｎｃｅｄｉｒｅｃｔｉｏｎｒｅｓｐｅｃｔｉｖｅｌｙｐｒｏｄｕｃｅｄｏｎｔｈｅ ｓｈｅｅｔｂｅｓｉｄｅｆａｓｔａｎｄｓｌｏｗｒｏｌｌｅｒｓ，ｔｈｅｒｅｆｏｒｅ，ｕｎｓ ｙｍｍｅｔｒｉｃｐｌａｓｔｉｃｆｌｏｗａｎｄｍａｃｒｏｓｃｏｐｉｃｓｔａｔｉｓｔｉｃａ ｌｕｎｓｙｍｍｅｔｒｙｏｆｔｅｘｔｕｒｅａｒｅｆｏｒｍｅｄ．Ｉｎｂａｃｋｗａｒｄｓｌｉ ｐｚｏｎｅｔｈｅｒｅａｒｅｔｈｅｓｈｅａｒｆｏｒｃｅｓｔｏｅｘｉｔｄｉｒｅｃｔｉｏｎｏ ｎｔｈｅｓｈｅｅｔｂｅｓｉｄｅｆａｓｔａｎｄｓｌｏｗｒｏｌｌｅｒｓ，ｔｈｅｙｃａｎｓｅ ｐａｒａｔｅｌｙｉｎｃｒｅａｓｅａｎｄｄｅｃｒｅａｓｅｕｎｓｙｍｍｅｔｒｉｃｐｌａｓｔ ｉｃｆｌｏｗｓａｎｄｔｈｅｓｙｍｍｅｔｒｙｏｆｔｅｘｔｕｒｅｏｎｔｈｅｆａｓｔａｎｄｓ ｌｏｗｒｏｌｌｅｒｓ．Ｉｎｓｉｄｅｏｆｔｈｅｓｈｅｅｔ，ｄｉｆｆｅｒｅｎｔｓｈｅａｒｆ ｏｒｃｅｓｗｈｉｃｈａｒｅｗｅａｋｅｒｔｈａｎｔｈａｔｏｆｓｕｒｆａｃｅｓａｒｅｐｒｏｄｕｃｅｄａｎｄｒｅｓｕｌｔｉｎｗｅａｋｅｒｉｎｔｅｎｓｉｔｙａｎｄｔｈｅｕｎｓｙｍｍｅｔｒｙｏｆｔｅｘｔｕｒｅ．Ｔｈｒｏｕｇｈｔｈｅｕｎｓｙｍｍｅｔｒｙｉｎ１ｌａｙｅｒｉｓｔｈｅｓｔｒｏｎｇｅｓｔ，ｂｕｔｔｈｅｔｅｘｔｕｒｅｂｅｓｉｄｅｔｈｅｓｌｏｗｒｏｌ
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